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  • Accessible aspects of 2-category theory
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-08-07
    John Bourke

    Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the structure of monoidal, but not strict monoidal, categories) then the 2-category in question is accessible. Furthermore, we explore the flexible limits that such 2-categories

    更新日期:2020-08-08
  • Symmetric decomposition of the associated graded algebra of an Artinian Gorenstein algebra
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Anthony Iarrobino; Pedro Macias Marques

    We study the symmetric subquotient decomposition of the associated graded algebras A⁎ of a non-homogeneous commutative Artinian Gorenstein (AG) algebra A. This decomposition arises from the stratification of A⁎ by a sequence of ideals A⁎=CA(0)⊃CA(1)⊃⋯ whose successive quotients Q(a)=C(a)/C(a+1) are reflexive A⁎ modules. These were introduced by the first author [47], [48], developed in the Memoir [49]

    更新日期:2020-08-04
  • Pretorsion theories in general categories
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-22
    Alberto Facchini; Carmelo Finocchiaro; Marino Gran

    We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair (T, F) of full replete subcategories in a category C, the corresponding full subcategory Z=T∩F of trivial objects in C. The morphisms which factor through Z are called Z-trivial, and these form an ideal of morphisms, with respect to which one can define Z-prekernels, Z-precokernels

    更新日期:2020-08-03
  • Betti numbers of Koszul algebras defined by four quadrics
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-25
    Paolo Mantero; Matthew Mastroeni

    Let I be an ideal generated by quadrics in a standard graded polynomial ring S over a field. A question of Avramov, Conca, and Iyengar asks whether the Betti numbers of R=S/I over S can be bounded above by binomial coefficients on the minimal number of generators of I if R is Koszul. This question has been answered affirmatively for Koszul algebras defined by three quadrics and Koszul almost complete

    更新日期:2020-07-31
  • Classical limit of quantum Borcherds-Bozec algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-16
    Zhaobing Fan; Seok-Jin Kang; Young Rock Kim; Bolun Tong

    Let g be a Borcherds-Bozec algebra, U(g) be its universal enveloping algebra and Uq(g) be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of Uq(g) is isomorphic to U(g) as Hopf algebras. Thus, Uq(g) can be regarded as a quantum deformation of U(g). We also provide explicit formulas for the commutation relations among the generators of Uq(g).

    更新日期:2020-07-29
  • Lie algebras of vertical derivations on semiaffine varieties with torus actions
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Ivan Arzhantsev; Alvaro Liendo; Taras Stasyuk

    Let X be a normal variety endowed with an algebraic torus action. An additive group action α on X is called vertical if a general orbit of α is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of α in Aut(X). Our first result in this paper is a classification of vertical additive group actions on X under the assumption that X is proper over an

    更新日期:2020-07-29
  • Invariance properties of coHochschild homology
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Kathryn Hess; Brooke Shipley

    The notion of Hochschild homology of a dg algebra admits a natural dualization, the coHochschild homology of a dg coalgebra, introduced in [23] as a tool to study free loop spaces. In this article we prove “agreement” for coHochschild homology, i.e., that the coHochschild homology of a dg coalgebra C is isomorphic to the Hochschild homology of the dg category of appropriately compact C-comodules, from

    更新日期:2020-07-27
  • Algebraic K-theory of generalized free products and functors Nil
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-23
    Pierre Vogel

    In this paper, we extend Waldhausen's results on algebraic K-theory of generalized free products in a more general setting and we give some properties of the Nil functors. As a consequence, we get new groups with trivial Whitehead groups.

    更新日期:2020-07-27
  • Algebras with finite relative dominant dimension and almost n-precluster tilting modules
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Shen Li; Shunhua Zhang

    In this paper, we investigate the relative dominant dimension with respect to an injective module and characterize the algebras with finite relative dominant dimension. As an application, we introduce a generalization of n-precluster tilting modules and use this to characterize a class of algebras including the class of n-minimal Auslander-Gorenstein algebras. Moreover, we give a description of the

    更新日期:2020-07-23
  • Seshadri constants and Okounkov bodies revisited
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-13
    Jinhyung Park; Jaesun Shin

    In recent years, the interaction between the local positivity of divisors and Okounkov bodies has attracted considerable attention, and there have been attempts to find a satisfactory theory of positivity of divisors in terms of convex geometry of Okounkov bodies. Many interesting results in this direction have been established by Choi–Hyun–Park–Won [4] and Küronya–Lozovanu [17], [18], [19] separately

    更新日期:2020-07-21
  • Trace identities and almost polynomial growth
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Antonio Ioppolo; Plamen Koshlukov; Daniela La Mattina

    In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: D2, the algebra of 2×2 diagonal matrices and C2, the algebra of 2×2 matrices generated by e11+e22 and e12. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties

    更新日期:2020-07-21
  • Local Gorenstein duality for cochains on spaces
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Tobias Barthel; Natàlia Castellana; Drew Heard; Gabriel Valenzuela

    We investigate when a commutative ring spectrum R satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein duality along morphisms of k-algebras. Our main examples are of the form R=C⁎(X;k), the ring spectrum of cochains on a space X for a field k. In particular, we establish

    更新日期:2020-07-21
  • Minimal log discrepancies of determinantal varieties via jet schemes
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Devlin Mallory

    We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs (Dk,∑αiDki) consisting of a determinantal variety (of square matrices) and an R-linear sum of determinantal subvarieties. Our result implies the semicontinuity conjecture for minimal log discrepancies of such pairs. For these computations, we use the description of minimal log discrepancies

    更新日期:2020-07-21
  • Low-degree rational curves on hypersurfaces in projective spaces and their fan degenerations1
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-14
    Ziv Ran

    We study rational curves on general Fano hypersurfaces in projective space, mostly by degenerating the hypersurface along with its ambient projective space to reducible varieties. We prove results on existence of low-degree rational curves with balanced normal bundle, and reprove some results on irreducibility of spaces of rational curves of low degree.

    更新日期:2020-07-21
  • On certain linearized polynomials with high degree and kernel of small dimension
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-14
    Olga Polverino; Giovanni Zini; Ferdinando Zullo

    Let f be the Fq-linear map over Fq2n defined by x↦x+axqs+bxqn+s with gcd⁡(n,s)=1. It is known that the kernel of f has dimension at most 2, as proved by Csajbók et al. in [9]. For n big enough, e.g. n≥5 when s=1, we classify the values of b/a such that the kernel of f has dimension at most 1. To this aim, we translate the problem into the study of some algebraic curves of small degree with respect

    更新日期:2020-07-21
  • Geodesic normal forms and Hecke algebras for the complex reflection groups G(de,e,n)
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Georges Neaime

    We establish geodesic normal forms for the general series of complex reflection groups G(de,e,n) by using the presentations of Corran–Picantin and Corran–Lee–Lee of G(e,e,n) and G(de,e,n) for d>1, respectively. This requires the elaboration of a combinatorial technique in order to explicitly determine minimal word representatives of the elements of G(de,e,n). Using these geodesic normal forms, we construct

    更新日期:2020-07-21
  • Homotopy Types of Abstract Elementary Classes
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-21
    Tim Campion; Jinhe Ye

    We prove that for any homotopy type X, there is an abstract elementary class C, with joint embedding, almagamation and no maximal models such that the classifying space realizes the homotopy type X. We provide a few explicit examples.

    更新日期:2020-07-21
  • A characterization of weakly Schreier extensions of monoids
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Peter F. Faul

    A split extension of monoids with kernel k:N→G, cokernel e:G→H and splitting s:H→G is Schreier if there exists a unique set-theoretic map q:G→N such that for all g∈G, g=kq(g)⋅se(g). Schreier extensions have a complete characterization and have been shown to correspond to monoid actions of H on N. If the uniqueness requirement of q is relaxed, the resulting split extension is called weakly Schreier

    更新日期:2020-07-20
  • The algebraic structure of left semi-trusses
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-07
    Ilaria Colazzo; Arne Van Antwerpen

    The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative “distributive” laws were defined. In an effort to study these “left distributive” laws and the interaction they entail on the algebraic structures, Brzeziński introduced skew left trusses and left semi-trusses. In particular

    更新日期:2020-07-20
  • On the universal completion of pointfree function spaces
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-17
    Imanol Mozo Carollo

    This paper approaches the construction of the universal completion of the Riesz space C(L) of continuous real functions on a completely regular frame L in two different ways. Firstly as the space of continuous real functions on the Booleanization of L. Secondly as the space of nearly finite Hausdorff continuous functions on L. The former has no counterpart in the classical theory, as the Booleanization

    更新日期:2020-07-20
  • On completion of unimodular rows over polynomial extension of finitely generated rings over Z
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Sampat Sharma

    In this article, we prove that if R is a finitely generated ring over Z of dimension d,d≥2,1d!∈R, then any unimodular row over R[X] of length d+1 can be mapped to a factorial row by elementary transformations.

    更新日期:2020-07-20
  • On the Hochschild homology of smash biproducts
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    A. Kaygun; S. Sütlü

    We develop a new spectral sequence in order to calculate the Hochschild homology of smash biproducts (also called the twisted tensor products) of unital associative algebras A#B provided one of A or B has Hochschild dimension less than 2. We use this spectral sequence to calculate Hochschild homology of the algebra Mq(2) of quantum 2×2-matrices.

    更新日期:2020-07-20
  • Noetherian rings of low global dimension and syzygetic prime ideals
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-15
    Francesc Planas-Vilanova

    Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every prime ideal of R is syzygetic. As a consequence, we derive a characterization of these rings using the André-Quillen homology.

    更新日期:2020-07-20
  • The continuous weak order
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-25
    Maria João Gouveia; Luigi Santocanale

    The set of permutations on a finite set can be given the lattice structure known as the weak Bruhat order. This lattice structure is generalized to the set of words on a fixed alphabet Σ={x,y,z,…}, where each letter has a fixed number of occurrences. These lattices are known as multinomial lattices and, when card(Σ)=2, as lattices of lattice paths. By interpreting the letters x,y,z,… as axes, these

    更新日期:2020-07-14
  • Locally finite continuations and Coxeter groups of infinite ranks
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-27
    Bernhard Mühlherr; Koji Nuida

    An involution r in a Coxeter group W is called an intrinsic reflection of W if r∈SW for each Coxeter generating set S of W. In recent joint work with R.B. Howlett [13] we determined all intrinsic reflections in finitely generated Coxeter groups. In the present paper we extend this result to the infinite rank case. An important tool in [13] is the notion of the finite continuation of an involution that

    更新日期:2020-07-10
  • Corrigendum to “Polyhedral divisors and torus actions of complexity one over arbitrary fields” [J. Pure Appl. Algebra 219 (6) (2015) 2015–2045]
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-07-04
    Kevin Langlois

    Statement [1, Lemma 5.9] is false in general unless if we assume that the algebraic torus G:=T/GE/k is quasi-split.

    更新日期:2020-07-06
  • Every finite abelian group is a subgroup of the additive group of a finite simple left brace
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-26
    F. Cedó; E. Jespers; J. Okniński

    Left braces, introduced by Rump, have turned out to provide an important tool in the study of set-theoretic solutions of the quantum Yang–Baxter equation. In particular, they have allowed to construct several new families of solutions. A left brace (B,+,⋅) is a structure determined by two group structures on a set B: an abelian group (B,+) and a group (B,⋅), satisfying certain compatibility conditions

    更新日期:2020-07-03
  • Virtual complete intersections in P1×P1
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Jiyang Gao; Yutong Li; Michael C. Loper; Amal Mattoo

    The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces P1×P1, we investigate which sets of points have a virtual resolution that is a Koszul complex on a regular sequence. This paper provides conditions on sets of points; some of which guarantee the points have this property, and

    更新日期:2020-07-03
  • Duality of Lusztig and RTT integral forms of Uv(Lsln)
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Alexander Tsymbaliuk

    We show that the Lusztig integral form is dual to the RTT integral form of the type A quantum loop algebra with respect to the new Drinfeld pairing, by utilizing the shuffle algebra realization of the former and the PBWD bases of the latter obtained in [13].

    更新日期:2020-06-25
  • Large orbit sizes in finite group actions
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Guohua Qian; Yong Yang

    In this paper, we study the relations of the sizes of various sections of finite linear groups and the largest orbit size of the linear group actions. We also study various applications of those orbit theorems.

    更新日期:2020-06-25
  • Dualizing involutions on the metaplectic GL(2)
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Kumar Balasubramanian; Ajit Bhand

    Let F be a non-Archimedean local field of characteristic zero. Let G=GL(2,F) and G˜=GL˜(2,F) be the metaplectic group. Let τ be the standard involution on G. A well known theorem of Gelfand and Kazhdan says that the standard involution takes any irreducible admissible representation of G to its contragredient. In such a case, we say that τ is a dualizing involution. In this paper, we show that any

    更新日期:2020-06-25
  • Arithmetic actions on cyclotomic function fields
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Aristides Kontogeorgis; Jacob Kenneth Ward

    We derive the group structure for cyclotomic function fields obtained by applying the Carlitz action for extensions of an initial constant field. The tame and wild structures are isolated to describe the Galois action on differentials. We show that the associated invariant rings are not polynomial.

    更新日期:2020-06-25
  • On the non-neutral component of outer forms of the orthogonal group
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Uriya A. First

    Let (A,σ) be a central simple algebra with an orthogonal involution. It is well-known that O(A,σ) contains elements of reduced norm −1 if and only if the Brauer class of A is trivial. We generalize this statement to Azumaya algebras with orthogonal involution over semilocal rings, and show that the “if” part fails if one allows the base ring to be arbitrary.

    更新日期:2020-06-25
  • Abelian quandles and quandles with abelian structure group
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Victoria Lebed; Arnaud Mortier

    Sets with a self-distributive operation (in the sense of (a◃b)◃c=(a◃c)◃(b◃c)), in particular quandles, appear in knot and braid theories, Hopf algebra classification, the study of the Yang–Baxter equation, and other areas. An important invariant of quandles is their structure group. The structure group of a finite quandle is known to be either “boring” (free abelian), or “interesting” (non-abelian

    更新日期:2020-06-25
  • General affine adjunctions, Nullstellensätze, and dualities
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Olivia Caramello; Vincenzo Marra; Luca Spada

    We introduce and investigate a category-theoretic abstraction of the standard “system-solution” adjunction in affine algebraic geometry. We then look further into these geometric adjunctions at different levels of generality, from syntactic categories to (possibly infinitary) equational classes of algebras. In doing so, we discuss the relationships between the dualities induced by our framework and

    更新日期:2020-06-25
  • On infinite variants of De Morgan law in locale theory
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Igor Arrieta

    A locale, being a complete Heyting algebra, satisfies De Morgan law (a∨b)⁎=a⁎∧b⁎ for pseudocomplements. The dual De Morgan law (a∧b)⁎=a⁎∨b⁎ (here referred to as the second De Morgan law) is equivalent to, among other conditions, (a∨b)⁎⁎=a⁎⁎∨b⁎⁎, and characterizes the class of extremally disconnected locales. This paper presents a study of the subclasses of extremally disconnected locales determined

    更新日期:2020-06-23
  • Endoregular modules
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    D.D. Anderson; J.R. Juett

    We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative

    更新日期:2020-06-23
  • Some classes of abstract simplicial complexes motivated by module theory
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    G. Chiaselotti; F. Infusino

    In this paper we analyze some classes of abstract simplicial complexes relying on algebraic models arising from module theory. To this regard, we consider a left-module on a unitary ring and find models of abstract complexes and related set operators having specific regularity properties, which are strictly interrelated to the algebraic properties of both the module and the ring. Next, taking inspiration

    更新日期:2020-06-23
  • Parabolic subgroups in FC-type Artin groups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Rose Morris-Wright

    Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping

    更新日期:2020-06-23
  • Quasi-hereditary covers of higher zigzag algebras of type A
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Gabriele Bocca

    In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Δ, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Δ-Koszul

    更新日期:2020-06-23
  • Periods of generalized Fermat curves
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Yerko Torres-Nova

    Let k,n≥2 be integers. A generalized Fermat curve of type (k,n) is a compact Riemann surface S that admits a subgroup of conformal automorphisms H≤Aut(S) isomorphic to Zkn, such that the quotient surface S/H is biholomorphic to the Riemann sphere Cˆ and has n+1 branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from

    更新日期:2020-06-23
  • On some properties of symplectic Grothendieck polynomials
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Eric Marberg; Brendan Pawlowski

    Grothendieck polynomials, introduced by Lascoux and Schützenberger, are certain K-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the K-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and

    更新日期:2020-06-23
  • The Duskin nerve of 2-categories in Joyal's cell category Θ2
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-17
    Viktoriya Ozornova; Martina Rovelli

    We give an explicit and purely combinatorial description of the Duskin nerve of any (r+1)-point suspension 2-category, and in particular of any 2-category belonging to Joyal's cell category Θ2.

    更新日期:2020-06-23
  • Quasi-bimonads and their representations
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-16
    Xiaohui Zhang; Xiaofan Zhao; Wei Wang

    In this paper quasi-bimonads on a monoidal category are introduced and investigated. Quasi-bimonads generalize quasi-bialgebras to a non-braided setting. We discuss their representations and investigate the R-matrix of a quasi-bimonad. Such an R-matrix provides a new solution of the version of the Yang-Baxter equation adapted to the situation. We also introduce an equivalent relation on (quasitriangular)

    更新日期:2020-06-23
  • Lie–Rinehart and Hochschild cohomology for algebras of differential operators
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-18
    Francisco Kordon; Thierry Lambre

    Let (S,L) be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the algebra and the Hochschild cohomology of S with values on M. After giving a convenient description

    更新日期:2020-06-18
  • Corrigendum to “Intrinsic alegebraic entropy” [J. Pure Appl. Algebra 219 (7) (2015) 2933–2961]
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-06-11
    Daniele Toller; Simone Virili

    We correct an argument in the proof of the Logarithmic Law for the intrinsic algebraic entropy, published as Lemma 3.12 in the article: D. Dikranjan, A. Giordano Bruno, L. Salce, S. Virili. Intrinsic algebraic entropy, J. Pure Appl. Algebra 219 (2015) 2933–2961.

    更新日期:2020-06-11
  • Critical loci in computer vision and matrices dropping rank in codimension one
    J. Pure Appl. Algebra (IF 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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 0.77) 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
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