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  • Critical loci in computer vision and matrices dropping rank in codimension one
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-26
    Marina Bertolini; Gian Mario Besana; Roberto Notari; Cristina Turrini

    Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable 4×3 matrices, N, of linear forms. Such loci are classified in this paper, in the case in which N drops rank in codimension one, giving rise to reducible varieties. This rests on the complete classification of matrices of size (n+1)×n for n≤3

    更新日期:2020-05-26
  • Homotopy invariants of singularity categories
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-21
    Sira Gratz; Greg Stevenson

    We present a method for computing A1-homotopy invariants of singularity categories of rings admitting suitable gradings. Using this we describe any such invariant, e.g. homotopy K-theory, for the stable categories of self-injective algebras admitting a connected grading. A remark is also made concerning the vanishing of all such invariants for cluster categories of type A2n quivers.

    更新日期:2020-05-21
  • Darboux-Jouanolou integrability over arbitrary fields
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-19
    Edileno de Almeida Santos; Sergio Rodrigues

    We prove a Darboux-Jouanolou type theorem on the algebraic integrability of polynomial differential 1-forms over arbitrary fields.

    更新日期:2020-05-19
  • On base loci of higher fundamental forms of toric varieties
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Antonio Laface; Luca Ugaglia

    We study the base locus of the higher fundamental forms of a projective toric variety X at a general point. More precisely we consider the closure X of the image of a map (C⁎)k→Pn, sending t to the vector of Laurent monomials with exponents p0,…,pn∈Zk. We prove that the m-th fundamental form of such an X at a general point has non empty base locus if and only if the points pi lie on a suitable degree-m

    更新日期:2020-05-18
  • BGG complexes in singular blocks of category O
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Volodymyr Mazorchuk; Rafael Mrđen

    Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category O. We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to be exact. In the Koszul dual picture, exactness of BGG complexes is expressed as a certain condition on a generalized Verma flag of an indecomposable projective object in the

    更新日期:2020-05-18
  • On Einstein Lorentzian nilpotent Lie groups
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Mohamed Boucetta; Oumaima Tibssirte

    In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie groups up to dimension 5 endowed with a Lorentzian Einstein left invariant metric have

    更新日期:2020-05-18
  • Quantum Weyl algebras and reflection equation algebras at a root of unity
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Nicholas Cooney; Iordan Ganev; David Jordan

    We compute the center and Azumaya locus in the simplest non-abelian examples of quantized multiplicative quiver varieties at a root of unity: quantum Weyl algebras of rank N, and quantum differential operators on the quantum group GL2. These examples illustrate in elementary terms much more general phenomena explored further in [8].

    更新日期:2020-05-18
  • Elementary doctrines as coalgebras
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Jacopo Emmenegger; Fabio Pasquali; Giuseppe Rosolini

    Lawvere's hyperdoctrines mark the beginning of applications of category theory to logic. In particular, existential elementary doctrines proved essential to give models of non-classical logics. The clear connection between (typed) logical theories and certain Pos-valued functors is exemplified by the embedding of the category of elementary doctrines into that of primary doctrines, which has a right

    更新日期:2020-05-18
  • An effective proof of the Cartan formula: The even prime
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Anibal M. Medina-Mardones

    The Cartan formula encodes the relationship between the cup product and the action of the Steenrod algebra in Fp-cohomology. In this work, we present an effective proof of the Cartan formula at the cochain level when the field is F2. More explicitly, for an arbitrary pair of cocycles and any non-negative integer, we construct a natural coboundary that descends to the associated instance of the Cartan

    更新日期:2020-05-18
  • A stable version of Harbourne's Conjecture and the containment problem for space monomial curves
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Eloísa Grifo

    The symbolic powers I(n) of a radical ideal I in a polynomial ring consist of the functions that vanish up to order n in the variety defined by I. These do not necessarily coincide with the ordinary algebraic powers In, but it is natural to compare the two notions. The containment problem consists of determining the values of n and m for which I(n)⊆Im holds. When I is an ideal of height 2 in a regular

    更新日期:2020-05-18
  • A version of Putinar's Positivstellensatz for cylinders
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-18
    Paula Escorcielo; Daniel Perrucci

    We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type S×R with S={x¯∈Rn|g1(x¯)≥0,…,gs(x¯)≥0} such that the quadratic module generated by g1,…,gs in R[X1,…,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f∈R[X1,…,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,…,gs

    更新日期:2020-05-18
  • A geometric realization of socle-projective categories for posets of type A
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-15
    Ralf Schiffler; Robinson-Julian Serna

    This paper establishes a link between the theory of cluster algebras and the theory of representations of partially ordered sets. We introduce a class of posets by requiring avoidance of certain types of peak-subposets and show that these posets can be realized as the posets of quivers of type A with certain additional arrows. This class of posets is therefore called posets of type A. We then give

    更新日期:2020-05-15
  • On the Hilbert function of Gorenstein algebras of socle degree four
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Armando Cerminara; Rodrigo Gondim; Giovanna Ilardi; Giuseppe Zappalà

    The first example of a non unimodal Gorenstein h-vector was given by Stanley, it is (1,13,12,13,1). In [14] the authors showed that Stanley's example is optimal, i.e., the vector (1,12,11,12,1) is not a Gorenstein h-vector. Our main result is a generalization of this result. We also give a simple proof of Stanley's conjecture on the asymptotic behavior of the Hilbert function in socle degree four.

    更新日期:2020-05-14
  • The algebraic K-theory of the projective line associated with a strongly Z-graded ring
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Thomas Hüttemann; Tasha Montgomery

    A Laurent polynomial ring R0[t,t−1] with coefficients in a unital ring determines a category of quasi-coherent sheaves on the projective line over R0; its K-theory is known to split into a direct sum of two copies of the K-theory of R0. In this paper, the result is generalised to the case of an arbitrary strongly Z-graded ring R in place of the Laurent polynomial ring. The projective line associated

    更新日期:2020-05-14
  • Zero-divisor placement, a condition of Camillo, and the McCoy property
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Jongwook Baeck; Nam Kyun Kim; Yang Lee; Pace P. Nielsen

    The rings for which any polynomial with a nonzero right annihilator must have a nonzero constant right annihilator are called the right McCoy rings. This class of rings includes the duo, reversible, polynomially semicommutative, and Armendariz rings, among others. In this paper we introduce a new condition, strictly generalizing the reversible property, which still implies the McCoy condition. We call

    更新日期:2020-05-14
  • Unique factorization property of non-unique factorization domains II
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Gyu Whan Chang; Andreas Reinhart

    Let D be an integral domain. A nonzero nonunit a of D is called a valuation element if there is a valuation overring V of D such that aV∩D=aD. We say that D is a valuation factorization domain (VFD) if each nonzero nonunit of D can be written as a finite product of valuation elements. In this paper, we study some ring-theoretic properties of VFDs. Among other things, we show that (i) a VFD D is Schreier

    更新日期:2020-05-14
  • Relative Brauer groups and étale cohomology
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Vivek Sadhu

    In this article, we construct a natural group homomorphismθ:Br(f)→Het1(S,f⁎OX×/OS×) for a faithful affine map f:X→S of noetherian schemes. Here Br(f) denotes the relative Brauer group of f. We also prove Br(f)=0 whenever f:A↪B is a subintegral extension of noetherian Q-algebras. Furthermore, we prove a relative version of Kummer's exact sequence.

    更新日期:2020-05-14
  • Approximation results of Artin-Tougeron-type for general filtrations and for Cr-equations
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Genrich Belitskii; Alberto F. Boix; Dmitry Kerner

    Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, {Ij}, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to Cr-rings, for 2≤r≤∞. As an auxiliary step we establish the surjectivity of the completion map

    更新日期:2020-05-14
  • A relative Segre zeta function
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Grayson Jorgenson

    The choice of a homogeneous ideal in a polynomial ring defines a closed subscheme Z in a projective space as well as an infinite sequence of cones over Z in progressively higher dimension projective spaces. Recent work of Aluffi introduces the Segre zeta function, a rational power series with integer coefficients which captures the relationship between the Segre class of Z and those of its cones. The

    更新日期:2020-05-14
  • Irreducible tensor products for alternating groups in characteristics 2 and 3
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Lucia Morotti

    In this paper we study irreducible tensor products of representations of alternating groups in characteristic 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify irreducible tensor products where neither factor in the product is a basic spin module. In characteristic 2 we also give some necessary conditions for the tensor

    更新日期:2020-05-14
  • Projective bundles enveloping rational conic fibrations and osculation
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Antonio Lanteri; Raquel Mallavibarrena

    Motivated by previous research on the osculation for special varieties, we investigate rational conic fibrations in connection with their enveloping projective bundles with the aim of comparing their inflectional loci. Specific existence results for such pairs are established. As a consequence, the possible various numerical characters of the pairs involved for low values of the sectional genus are

    更新日期:2020-05-14
  • Seshadri constants of the anticanonical divisors of Fano manifolds with large index
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-05-14
    Jie Liu

    Seshadri constants, introduced by Demailly, measure the local positivity of a nef divisor at a point. In this paper, we compute the Seshadri constants of the anticanonical divisors of Fano manifolds with coindex at most 3 at a very general point. As a consequence, if X is a nonsingular Fano threefold which is very general in its deformation family, then ε(X,−KX;x)≤1 for all points x∈X if and only if

    更新日期:2020-05-14
  • On the local cartesian closure of exact completions
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-30
    Jacopo Emmenegger

    This paper presents a necessary and sufficient condition on a category C with weak finite limits for its exact completion Cex to be (locally) cartesian closed. A paper by Carboni and Rosolini already claimed such a characterisation using a different property on C, but we shall show that weak finite limits are not enough for their proof to go through. We shall also indicate how to strengthen the hypothesis

    更新日期:2020-04-30
  • Circulant matrices and Galois-Togliatti systems
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-29
    Pietro De Poi; Emilia Mezzetti; Mateusz Michałek; Rosa Maria Miró-Roig; Eran Nevo

    The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we solve a conjecture stated in [17] concerning the minimality of GT-systems.

    更新日期:2020-04-29
  • Some extension algebras for standard modules over KLR algebras of type A
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-24
    Doeke Buursma; Alexander Kleshchev; David J. Steinberg

    Khovanov-Lauda-Rouquier algebras Rθ of finite Lie type are affine quasihereditary with standard modules Δ(π) labeled by Kostant partitions of θ. Let Δ be the direct sum of all standard modules. It is known that the Yoneda algebra Eθ:=ExtRθ⁎(Δ,Δ) carries a structure of an A∞-algebra which can be used to reconstruct the category of standardly filtered Rθ-modules. In this paper, we explicitly describe

    更新日期:2020-04-24
  • Cotorsion pairs and a K-theory localization theorem
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Maru Sarazola

    We show that a complete hereditary cotorsion pair (C,C⊥) in an exact category E, together with a subcategory Z⊆E containing C⊥, determines a Waldhausen category structure on the exact category C, in which Z is the class of acyclic objects. This allows us to prove a new version of Quillen's Localization Theorem, relating the K-theory of exact categories A⊆B to that of a cofiber. The novel idea in our

    更新日期:2020-04-23
  • Toroidalization of locally toroidal morphisms from n-folds to 3-folds
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Razieh Ahmadian

    Toroidal varieties (called toroidal embeddings in [KKMS]), roughly speaking, are algebraic varieties that are locally (formally) toric in structure, and toroidal morphisms are those morphisms of varieties which are locally determined by toric morphisms. A toroidal lifting of a morphism φ:X→Y of algebraic varieties, which can be obtained by performing sequences of blowups of nonsingular subvarieties

    更新日期:2020-04-23
  • The first and second fundamental theorems of invariant theory for the quantum general linear supergroup
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Yang Zhang

    We develop a non-commutative polynomial version of the invariant theory of the quantum general linear supergroup Uq(glm|n). A non-commutative Uq(glm|n)-module superalgebra Pr|sk|l is constructed, which is the quantum analogue of the supersymmetric algebra over Ck|l⊗Cm|n⊕Cr|s⊗(Cm|n)⁎. We analyse the structure of the subalgebra of Uq(glm|n)-invariants in Pr|sk|l by using a quantum super analogue of Howe

    更新日期:2020-04-23
  • The Left Localization Principle, completions, and cofree G-spectra
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Luca Pol; Jordan Williamson

    We show under mild hypotheses that a Quillen adjunction between stable model categories induces another Quillen adjunction between their left localizations, and we provide conditions under which the localized adjunction is a Quillen equivalence. Moreover, we show that in many cases the induced Quillen equivalence is symmetric monoidal. Using our results we construct a symmetric monoidal algebraic model

    更新日期:2020-04-23
  • Explicit Boij–Söderberg theory of ideals from a graph isomorphism reduction
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Alexander Engström; Laura Jakobsson; Milo Orlich

    In the origins of complexity theory Booth and Lueker showed that the question of whether two graphs are isomorphic or not can be reduced to the special case of chordal graphs. To prove that, they defined a transformation from graphs G to chordal graphs BL(G). The projective resolutions of the associated edge ideals IBL(G) are manageable and we investigate to what extent their Betti tables also tell

    更新日期:2020-04-23
  • Permutation modules for cellularly stratified algebras
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    Inga Paul

    Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for Brauer algebras. We generalise their construction to a wider class of algebras, namely cellularly stratified algebras, satisfying certain conditions. We give a decomposition into indecomposable summands, the Young modules, and show that permutation modules

    更新日期:2020-04-23
  • Commutativity in Jordan operator algebras
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-23
    John van de Wetering

    While Jordan algebras are commutative, operator commutativity will behave badly for a general non-associative Jordan algebra. When the product operators of two elements commute, the elements are said to operator commute. In some Jordan algebras operator commutation can be badly behaved, for instance having elements a and b operator commute, while a2 and b do not operator commute. In this paper we study

    更新日期:2020-04-23
  • Signature cocycles on the mapping class group and symplectic groups
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    Dave Benson; Caterina Campagnolo; Andrew Ranicki; Carmen Rovi

    Werner Meyer constructed a cocycle in H2(Sp(2g,Z);Z) which computes the signature of a closed oriented surface bundle over a surface. By studying properties of this cocycle, he also showed that the signature of such a surface bundle is a multiple of 4. In this paper, we study signature cocycles both from the geometric and algebraic points of view. We present geometric constructions which are relevant

    更新日期:2020-04-22
  • Wedge-direct sums of table algebras and applications to association schemes, II
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    Bangteng Xu

    Extensions of association schemes and table algebras have been studied in many papers in the last two decades. A remarkable operation (the Blau-construction) on two table algebras in [3] provides an important method to construct the extension of table algebras. The wedge-direct sum of a sequence of table algebras introduced in Part I (see [14]) is a useful tool for the study of structures and characterizations

    更新日期:2020-04-22
  • On the generalized Krull property in power series rings
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    Le Thi Ngoc Giau; Byung Gyun Kang; Phan Thanh Toan

    One open problem in commutative algebra and field arithmetic posed by Jarden is whether the power series ring R〚X〛 is a generalized Krull domain if R is a generalized Krull domain. Assuming R is a generalized Krull domain, Paran and Temkin proved that R〚X〛 is a generalized Krull domain if and only if R〚X〛 is a Krull domain. Hence, if R is a generalized Krull domain that is not a Krull domain, then

    更新日期:2020-04-22
  • On formations of monoids
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    Mário J.J. Branco; Gracinda M.S. Gomes; Jean-Éric Pin; Xaro Soler-Escrivà

    A formation of monoids is a class of finite monoids closed under taking quotients and subdirect products. Formations of monoids were first studied in connection with formal language theory, but in this paper, we come back to an algebraic point of view. We give two natural constructions of formations based on constraints on the minimal ideal and on the maximal subgroups of a monoid. Next we describe

    更新日期:2020-04-22
  • The abelian closure of an exact category
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    Wolfgang Rump

    The paper exhibits three constitutive exact subcategories of Adelman's free abelian category Ab(A) over a Quillen exact category A, which provide an intrinsic description of Ab(A) and encapsulate the mechanism of (finite or infinite) tilting. In general, two of these subcategories are left and right abelian, respectively, and a tilting adjunction takes place between them if they are abelian. The third

    更新日期:2020-04-22
  • On reflexivity and the Ascoli property for free locally convex spaces
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-22
    S. Gabriyelyan

    Let L(X) be the free locally convex space over a Tychonoff space X. If X is Dieudonné complete (for example, metrizable), then L(X) is a reflexive group if and only if X is discrete. We prove also that L(X) is an Ascoli space if and only if X is a countable discrete space.

    更新日期:2020-04-22
  • The first cohomology of sl(2,1) with coefficients in χ-reduced Kac modules and simple modules
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-21
    Shujuan Wang; Wende Liu

    Over a field of characteristic p>2, the first cohomology of the special linear Lie superalgebra sl(2,1) with coefficients in all χ-reduced Kac modules and simple modules is determined by use of the weight space decompositions of these modules relative to the standard Cartan subalgebra of sl(2,1).

    更新日期:2020-04-21
  • Codensity: Isbell duality, pro-objects, compactness and accessibility
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-09
    Ivan Di Liberti

    We study codensity monads T induced by (mostly small, mostly dense) full subcategories A⊂K. These monads behave quite similarly, we show some connections with the Isbell duality, pro-finite objects and compact spaces. We prove that they are quite unlikely to be accessible. Finally, we introduce the notion of generically idempotent monad and comment its properties.

    更新日期:2020-04-09
  • M-coextensive objects and the strict refinement property
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-08
    Michael Hoefnagel

    The notion of an M-coextensive object is introduced in an arbitrary category C, where M is a distinguished class of morphisms from C. This notion allows for a categorical treatment of the strict refinement property in universal algebra, and highlights its connection with extensivity in the sense of Carboni, Lack and Walters. If M is the class of product projections in a category C with finite products

    更新日期:2020-04-08
  • A prime-characteristic analogue of a theorem of Hartshorne-Polini
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-06
    Nicholas Switala; Wenliang Zhang

    Let R be an F-finite Noetherian regular ring containing an algebraically closed field k of positive characteristic, and let M be an F-finite F-module over R in the sense of Lyubeznik (for example, any local cohomology module of R). We prove that the Fp-dimension of the space of F-module morphisms M→E(R/m) (where m is any maximal ideal of R and E(R/m) is the R-injective hull of R/m) is equal to the

    更新日期:2020-04-06
  • Matlis category equivalences for a ring epimorphism
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-06
    Silvana Bazzoni; Leonid Positselski

    Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism u:R⟶U. Assuming that the ring epimorphism is homological of flat/projective dimension 1, we discuss the abelian categories of u-comodules and u-contramodules and construct the recollement of unbounded derived categories of R-modules, U-modules, and complexes of R-modules with u-co/contramodule

    更新日期:2020-04-06
  • Projective normality of torus quotients of flag varieties
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-06
    Arpita Nayek; S.K. Pattanayak; Shivang Jindal

    Let G=SLn(C) and T be a maximal torus in G. We show that the quotient T\\G/Pα1∩Pα2 is projectively normal with respect to the descent of a suitable line bundle, where Pαi is the maximal parabolic subgroup in G associated to the simple root αi, i=1,2. We give a degree bound of the generators of the homogeneous coordinate ring of T\\(G3,6)Tss(L2ϖ3). If G=Spin7, we give a degree bound of the generators

    更新日期:2020-04-06
  • Crossed products of Calabi-Yau algebras by finite groups
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-06
    Patrick Le Meur

    Let a finite group G act on a differential graded algebra A. This article presents necessary conditions and sufficient conditions for the skew group algebra A⁎G to be Calabi-Yau. In particular, when A is the Ginzburg dg algebra of a quiver with an invariant potential, then A⁎G is Calabi-Yau and Morita equivalent to a Ginzburg dg algebra. Some applications of these results are derived to compare the

    更新日期:2020-04-06
  • Third kind elliptic integrals and 1-motives
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-03
    Cristiana Bertolin

    In [4] we have showed that the Generalized Grothendieck's Period Conjecture applied to 1-motives, whose underlying semi-abelian variety is a product of elliptic curves and of tori, is equivalent to a transcendental conjecture involving elliptic integrals of the first and second kind, and logarithms of complex numbers. In this paper we investigate the Generalized Grothendieck's Period Conjecture in

    更新日期:2020-04-03
  • Remarks on projective normality for certain Calabi–Yau and hyperkähler varieties
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-03
    Jayan Mukherjee; Debaditya Raychaudhury

    We prove some results on effective very ampleness and projective normality for some varieties with trivial canonical bundle. In the first part we prove an effective projective normality result for an ample line bundle on regular smooth four-folds with trivial canonical bundle. More precisely we show that for a regular smooth four-fold with trivial canonical bundle, A⊗15 is projectively normal for A

    更新日期:2020-04-03
  • Restriction and extension of partial actions
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-03
    Dirceu Bagio; Antonio Paques; Héctor Pinedo

    Given a partial action α=(Ag,αg)g∈G of a connected groupoid G on a ring A and an object x of G, the isotropy group G(x) acts partially on the ideal Ax of A by the restriction of α. In this paper we investigate the following reverse question: under which conditions a partial group action of G(x) on an ideal of A can be extended to a partial groupoid action of G on A? The globalization problem and some

    更新日期:2020-04-03
  • Pure resolutions, linear codes, and Betti numbers
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-03
    Sudhir R. Ghorpade; Prasant Singh

    We consider the minimal free resolutions of Stanley-Reisner rings associated to linear codes and give an intrinsic characterization of linear codes having a pure resolution. We use this characterization to quickly deduce the minimal free resolutions of Stanley-Reisner rings associated to MDS codes as well as constant weight codes. We also deduce that the minimal free resolutions of Stanley-Reisner

    更新日期:2020-04-03
  • Loewy lengths of centers of blocks and exponents of defect groups
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-02
    Yoshihiro Otokita

    In this paper we study the Loewy structure of the center ZB of a block of a finite group with respect to an algebraically closed field of prime characteristic. We first state a new method for calculating the Loewy length LL(ZB) of ZB in terms of subsections and lower defect groups. By applying this result we give an upper bound of LL(ZB) which depends on the exponent of a defect group of B for some

    更新日期:2020-04-02
  • Norm coherence for descent of level structures on formal deformations
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-02
    Yifei Zhu

    We give a formulation for descent of level structures on deformations of formal groups and study the compatibility between descent and a norm construction. Under this framework, we generalize Ando's construction of H∞ complex orientations for Morava E-theories associated to the Honda formal groups over Fp. We show the existence and uniqueness of such an orientation for any Morava E-theory associated

    更新日期:2020-04-02
  • On the Prym map for cyclic covers of genus two curves
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-02
    Daniele Agostini

    The Prym map assigns to each covering of curves a polarized abelian variety. In the case of étale cyclic covers of curves of genus two, we show that the Prym map is ramified precisely on the locus of bielliptic covers. The key observation is that we can naturally associate to such a cover an abelian surface with a cyclic polarization, and then the codifferential of the Prym map can be interpreted in

    更新日期:2020-04-02
  • Generators of Koszul homology with coefficients in a J-closed module
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-02
    Rachel N. Diethorn

    We introduce a class of modules, called J-closed modules, inspired by the weak complete intersection ideals studied by Rahmati, Striuli, and Yang. We present explicit formulas for the generators of Koszul homology with coefficients in such modules. This generalizes work of Herzog and of Corso, Goto, Huneke, Polini, and Ulrich. We use these formulas to study connections between J-closed ideals and weak

    更新日期:2020-04-02
  • Tensor topology
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-01
    Pau Enrique Moliner; Chris Heunen; Sean Tull

    A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We show that under mild conditions subunits endow any monoidal category with a kind of topological intuition: there are well-behaved notions of restriction, localisation

    更新日期:2020-04-01
  • Quantum Borcherds-Bozec algebras and their integrable representations
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-04-01
    Seok-Jin Kang; Young Rock Kim

    We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a triangular decomposition and the category of integrable representations is semi-simple.

    更新日期:2020-04-01
  • Brown's criterion and classifying spaces for families
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-03-31
    Eduardo Martínez-Pedroza; Luis Jorge Sánchez Saldaña

    Let G be a group and F be a family of subgroups closed under conjugation and subgroups. A model for the classifying space EFG is a G-CW-complex X such that every isotropy group belongs to F, and for all H∈F the fixed point subspace XH is contractible. The group G is of type F-Fn if it admits a model for EFG with n-skeleton with compact orbit space. The main result of the article provides is a characterization

    更新日期:2020-03-31
  • Facets of congruence distributivity in Goursat categories
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-03-31
    Marino Gran; Diana Rodelo; Idriss Tchoffo Nguefeu

    We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories (which extend 3-permutable varieties) through variations of the Triangular and Trapezoid Lemmas involving reflexive

    更新日期:2020-03-31
  • Numerical root finding via Cox rings
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-03-23
    Simon Telen

    We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification X of (C∖{0})n. We homogenize the input equations to obtain a homogeneous ideal I in the Cox ring of X and generalize the eigenvalue, eigenvector theorem for root finding in affine space to compute homogeneous coordinates of the solutions.

    更新日期:2020-03-23
  • Fraction, restriction, and range categories from stable systems of morphisms
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-03-12
    S.N. Hosseini; A.R. Shir Ali Nasab; W. Tholen

    For a composition-closed and pullback-stable class S of morphisms in a category C containing all isomorphisms, we form the category Span(C,S) of S-spans (s,f) in C with first “leg” s lying in S, and give an alternative construction of its quotient category C[S−1] of S-fractions. Instead of trying to turn S-morphisms “directly” into isomorphisms, we turn them separately into retractions and into sections

    更新日期:2020-03-12
  • Higher Lawvere theories
    J. Pure Appl. Algebra (IF 0.797) Pub Date : 2020-03-12
    John D. Berman

    We survey Lawvere theories at the level of ∞-categories, as an alternative framework for higher algebra (rather than ∞-operads). From a pedagogical perspective, they make many key definitions and constructions less technical. They also play a prominent role in equivariant homotopy theory and its relatives. Our main result establishes a universal property for the ∞-category of Lawvere theories, which

    更新日期:2020-03-12
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