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  • On partial skew groupoid rings
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-10-12
    Dirceu Bagio; Antonio Paques; Héctor Pinedo

    Given a partial action α of a connected groupoid 𝒢 on an associative ring A we investigate under what conditions the partial skew groupoid ring A⋆α𝒢 can be realized as a partial skew group ring. In such a case, applications concerning to the separability, semisimplicity and Frobenius property of the ring extension A⊂A⋆α𝒢 as well as to the artinianity of A⋆α𝒢 are given.

    更新日期:2020-10-21
  • n-Permutability is not join-prime for n ≥ 5
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-10-10
    Gergő Gyenizse; Miklós Maróti; László Zádori

    Let 𝒱P be the variety generated by an order primal algebra of finite signature associated with a finite bounded poset P that admits a near-unanimity operation. Let Λ be a finite set of linear identities that does not interpret in 𝒱P. Let 𝒱Λ be the variety defined by Λ. We prove that 𝒱P∨𝒱Λ is n-permutable for some n. This implies that there is an n such that n-permutability is not join-prime in

    更新日期:2020-10-21
  • Computing subschemes of the border basis scheme
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-09-19
    Martin Kreuzer; Le Ngoc Long; Lorenzo Robbiano

    A good way of parameterizing zero-dimensional schemes in an affine space 𝔸Kn has been developed in the last 20 years using border basis schemes. Given a multiplicity μ, they provide an open covering of the Hilbert scheme Hilbμ(𝔸Kn) and can be described by easily computable quadratic equations. A natural question arises on how to determine loci which are contained in border basis schemes and whose

    更新日期:2020-10-21
  • On the complexity of the lattices of subvarieties and congruences
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    A. V. Kravchenko; A. M. Nurakunov; M. V. Schwidefsky

    We find sufficient conditions guaranteeing that for a quasivariety M of structures of finite type containing a B-class with respect to M, there exists a subquasivariety K⊆M and a structure 𝒜∈K such that the problems whether a finite lattice embeds into the lattice Lv(K) of K-varieties and into the lattice ConK𝒜 are undecidable.

    更新日期:2020-10-21
  • Gelfand–Tsetlin varieties for 𝔤𝔩n
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-09-02
    Germán Benitez

    Sergei Ovsienko proved that the Gelfand–Tsetlin variety for 𝔤𝔩n is equidimensional and the dimension of all irreducible components equals n(n−1)/2. This implies in particular the equidimensionality of the nilfiber of the (partial) Kostant–Wallach map. We generalize this result for the k-partial Kostant–Wallach map and prove that all its fibers are equidimensional of dimension n2−(k+1)n+k(k+1)/2.

    更新日期:2020-10-21
  • Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-30
    Dan Chen; Yan-Feng Luo; Yi Zhang; Yuan-Yuan Zhang

    Motivated by the formula of partial integration, we introduce the concept of Ω-Rota–Baxter algebras, which generalizes the Rota–Baxter algebras introduced by Baxter. We then construct free objects in the category of Ω-Rota–Baxter algebras, via a method of Gröbner–Shirshov bases.

    更新日期:2020-10-08
  • Truncated boolean representable simplicial complexes
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-30
    Stuart Margolis; John Rhodes; Pedro V. Silva

    We extend, in significant ways, the theory of truncated boolean representable simplicial complexes introduced in 2015. This theory, which includes all matroids, represents the largest class of finite simplicial complexes for which combinatorial geometry can be meaningfully applied.

    更新日期:2020-10-08
  • Formal language convexity in left-orderable groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    Hang Lu Su

    We propose a criterion for preserving the regularity of a formal language representation when passing from groups to subgroups. We use this criterion to show that the regularity of a positive cone language in a left-orderable group passes to its finite index subgroups, and to show that there exists no left order on a finitely generated acylindrically hyperbolic group such that the corresponding positive

    更新日期:2020-10-08
  • Factoring octonion polynomials
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-17
    Adam Chapman

    We provide an analogue of Wedderburn’s factorization method for central polynomials with coefficients in an octonion division algebra, and present an algorithm for fully factoring polynomials of degree n with n conjugacy classes of roots, counting multiplicities.

    更新日期:2020-10-08
  • On the enumeration and asymptotic growth of free quasigroup words
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-08
    Jonathan D. H. Smith; Stefanie G. Wang

    This paper counts the number of reduced quasigroup words of a particular length in a certain number of generators. Taking account of the relationship with the Catalan numbers, counting words in a free magma, we introduce the term peri-Catalan number for the free quasigroup word counts. The main result of this paper is an exact recursive formula for the peri-Catalan numbers, structured by the Euclidean

    更新日期:2020-10-08
  • Characters of Renner monoids and their Hecke algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    Andrew Hardt; Jared Marx-Kuo; Vaughan McDonald; John M. O’Brien; Alexander Vetter

    This paper gives a general algorithm for computing the character table of any Renner monoid Hecke algebra, by adapting and generalizing techniques of Solomon used to study the rook monoid. The character table of the Hecke algebra of the rook monoid (i.e. the Cartan type A Renner monoid) was computed earlier by Dieng et al. [2], using different methods. Our approach uses analogues of so-called A- and

    更新日期:2020-10-08
  • Sectional algebras of semigroupoid bundles
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    Luiz Gustavo Cordeiro

    In this paper, we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell (C∗-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be regarded as the sectional algebras of trivial (direct product) bundles. Several theorems which relate geometric and algebraic constructions — via the construction of

    更新日期:2020-10-07
  • The descending central series of higher commutators for simple algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-24
    Steven Weinell

    This paper characterizes the potential behaviors of higher commutators in a simple algebra.

    更新日期:2020-09-30
  • Random coxeter groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-20
    Angelica Deibel

    Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös–Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about the homology of the nerve of a random Coxeter group and results about when random

    更新日期:2020-09-30
  • An algorithm for a lifted Massey triple product of a smooth projective plane curve
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-09-24
    Younggi Lee; Jeehoon Park; Junyeong Park; Jaehyun Yim

    We provide an explicit algorithm to compute a lifted Massey triple product relative to a defining system for a smooth projective plane curve X defined by a homogeneous polynomial G(x̲) over a field. The main idea is to use the description (due to Carlson and Griffiths) of the cup product for H1(X,ℂ) in terms of the multiplications inside the Jacobian ring of G(x̲) and the Cech–deRham complex of X.

    更新日期:2020-09-25
  • Center of skew PBW extensions
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-09-19
    Oswaldo Lezama; Helbert Venegas

    In this paper we compute the center of many noncommutative algebras that can be interpreted as skew PBW extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.

    更新日期:2020-09-20
  • Binomial edge ideals of generalized block graphs
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    Arvind Kumar

    We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo–Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by m(G)+1, where m(G) is the number of minimal cut sets of the graph G and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices

    更新日期:2020-08-28
  • The solubility graph associated with a finite group
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    B. Akbari; Mark L. Lewis; J. Mirzajani; A. R. Moghaddamfar

    The solubility graph associated with a finite group G is a simple graph whose vertices are the elements of G, and there is an edge between two distinct elements x and y if and only if 〈x,y〉 is a soluble subgroup of G. We examine some properties of solubility graphs.

    更新日期:2020-08-28
  • Exterior and symmetric (co)homology of groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-28
    Valeriy G. Bardakov; Mikhail V. Neshchadim; Mahender Singh

    The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric (co)homologies. Finally, we derive restriction and corestriction homomorphisms for exterior cohomology.

    更新日期:2020-08-28
  • Distributive laws between the operads Lie and Com
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-08-20
    Murray Bremner; Vladimir Dotsenko

    Using methods of computer algebra, especially, Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet–Loday formula deforming the Poisson

    更新日期:2020-08-21
  • Exterior powers of the standard E6-module: An elementary approach
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-24
    A. M. Semenov; A. N. Zubkov

    For the standard 27-dimensional representation V of the exceptional group G of type E6 we prove that (SL(V),G) is a Donkin pair if and only if the characteristic of a ground field is greater than 13. We also develop an elementary approach to describe submodule structure of any exterior power of V.

    更新日期:2020-07-24
  • Hilbert series associated to symplectic quotients by SU2
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-24
    Hans-Christian Herbig; Daniel Herden; Christopher Seaton

    We compute the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an SU2-module and give an explicit expression for the first nonzero coefficient of the Laurent expansion of the Hilbert series at t=1. Our expression for the Hilbert series indicates an algorithm to compute it, and we give the output of this algorithm for all representations of dimension

    更新日期:2020-07-24
  • The binomial equivalence classes of finite words
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-07-14
    Marie Lejeune; Michel Rigo; Matthieu Rosenfeld

    Two finite words u and v are k-binomially equivalent if, for each word x of length at most k, x appears the same number of times as a subsequence (i.e., as a scattered subword) of both u and v. This notion generalizes abelian equivalence. In this paper, we study the equivalence classes induced by the k-binomial equivalence. We provide an algorithm generating the 2-binomial equivalence class of a word

    更新日期:2020-07-14
  • Symbolic powers of vertex cover ideals
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-06-24
    S. Selvaraja

    Let G be a finite simple graph and J(G) denote its vertex cover ideal in a polynomial ring over a field 𝕂. In this paper, we show that all symbolic powers of vertex cover ideals of certain vertex-decomposable graphs have linear quotients. Using these results, we give various conditions on a subset S of the vertices of G so that all symbolic powers of vertex cover ideals of G∪W(S), obtained from G

    更新日期:2020-06-24
  • The conjugacy problem for Higman’s group
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-06-20
    Owen Baker

    Higman’s group H=〈a,b,c,d|ba=b2,cb=c2,dc=d2,ad=a2〉 is a remarkable group with large (non-elementary) Dehn function. Higman constructed the group in 1951 to produce the first examples of infinite simple groups. Using finite state automata, and studying fixed points of certain finite state transducers, we show the conjugacy problem in H is decidable for all inputs. Diekert, Laun and Ushakov have recently

    更新日期:2020-06-20
  • Local and 2-local derivations of solvable Leibniz algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-06-18
    Shavkat Ayupov; Abror Khudoyberdiyev; Bakhtiyor Yusupov

    We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have 1 dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning 2-local derivations of such algebras

    更新日期:2020-06-18
  • Minimum degree of an A-identity of E ⊗ E
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-06-18
    Fernando Augusto Naves; Humberto Luiz Talpo

    Let F be a field of characteristic zero, algebraically closed and E be the unitary infinite-dimensional Grassmann F-algebra. Our aim is to determine the minimal degree of an A-polynomial satisfied by E⊗E. Also, we find an explicit A-identity of E⊗E.

    更新日期:2020-06-18
  • On growth of double cosets in hyperbolic groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-06-05
    Rita Gitik; Eliyahu Rips

    Let H be a hyperbolic group, A and B be subgroups of H, and gr(H,A,B) be the growth function of the double cosets AhB,h∈H. We prove that the behavior of gr(H,A,B) splits into two different cases. If A and B are not quasiconvex, we obtain that every growth function of a finitely presented group can appear as gr(H,A,B). We can even take A=B. In contrast, for quasiconvex subgroups A and B of infinite

    更新日期:2020-06-05
  • Conjugate subgroups and overgroups of Vn
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-30
    Casey Donoven; Feyishayo Olukoya

    We describe subgroups and overgroups of the generalized Thompson groups Vn which arise via conjugation by rational homeomorphisms of Cantor space. We specifically consider conjugating Vn by homeomorphisms induced by synchronizing transducers and their inverses. Our descriptions of the subgroups and overgroups use properties of the conjugating transducer to either restrict or augment the action of Vn

    更新日期:2020-03-30
  • Frobenius action on Carter subgroups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-27
    Güli̇n Ercan; İsmai̇l Ş. Güloğlu

    Let G be a finite solvable group and H be a subgroup of Aut(G). Suppose that there exists an H-invariant Carter subgroup F of G such that the semidirect product FH is a Frobenius group with kernel F and complement H. We prove that the terms of the Fitting series of CG(H) are obtained as the intersection of CG(H) with the corresponding terms of the Fitting series of G, and the Fitting height of G may

    更新日期:2020-03-27
  • On certain subgroups of the McCool group
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-23
    C. E. Kofinas

    For a positive integer n, with n≥2, let Fn be a free group of rank n and let IA(Fn) be the subgroup of the automorphism group of Fn consisting of all automorphisms which induce the identity on the abelianization of Fn. We write Mn+ and In for the upper McCool group and the partial inner automorphism group, respectively. We show that In is isomorphic to the quotient of Mn+1+ by its center and we prove

    更新日期:2020-03-23
  • Universal enveloping Poisson conformal algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-20
    P. S. Kolesnikov

    Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal

    更新日期:2020-03-20
  • Wilf’s conjecture in fixed multiplicity
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-13
    Winfried Bruns; Pedro García-Sánchez; Christopher O’Neill; Dane Wilburne

    We give an algorithm to determine whether Wilf’s conjecture holds for all numerical semigroups with a given multiplicity m, and use it to prove Wilf’s conjecture holds whenever m≤18. Our algorithm utilizes techniques from polyhedral geometry, and includes a parallelizable algorithm for enumerating the faces of any polyhedral cone up to orbits of an automorphism group. We also introduce a new method

    更新日期:2020-03-13
  • ℤ2 and ℤ-graded central polynomials of the Grassmann algebra
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-12
    Alan De Araújo Guimarães; Claudemir Fidelis; Plamen Koshlukov

    Let F be an infinite field of characteristic different from 2, and let E be the Grassmann algebra of a countable of dimensional F-vector space L. In this paper, we study the graded central polynomials of gradings on E by the groups ℤ2 and ℤ, where the basis of the vector space L is homogeneous. More specifically, we provide a basis for the TG-space of graded central polynomials for E, where the group

    更新日期:2020-03-12
  • Computing skew left braces of small orders
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-10
    Valeriy G. Bardakov; Mikhail V. Neshchadim; Manoj K. Yadav

    We improve Algorithm 5.1 of [Math. Comp. 86 (2017) 2519–2534] for computing all nonisomorphic skew left braces, and enumerate left braces and skew left braces of orders up to 868 with some exceptions. Using the enumerated data, we state some conjectures for further research.

    更新日期:2020-03-10
  • Vanishing-off subgroups and supercharacter theory products
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-03-05
    Shawn T. Burkett; Mark L. Lewis

    In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, we give a character theoretic characterization that allows us to conclude that one may determine if a supercharacter theory is a Δ-product or ∗-product from the values of its corresponding supercharacters.

    更新日期:2020-03-05
  • Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-27
    Paula Macedo Lins de Araujo

    This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as rationality and functional equations. Here, we calculate such bivariate zeta functions of three infinite families of nilpotent groups of class 2 generalizing the Heisenberg

    更新日期:2020-02-27
  • Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-25
    H. Ahmed; U. Bekbaev; I. Rakhimov

    All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classifications of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of isomorphism classes of all simple two-dimensional algebras is given. In the study of ideals and subalgebras, the number of them depends on roots of certain system of polynomials

    更新日期:2020-02-25
  • The index of small length sequences
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-19
    David J. Grynkiewicz; Uzi Vishne

    Let n≥2 be a fixed integer. Define (x)n to be the unique integer in the range 0≤(x)n

    更新日期:2020-02-19
  • Super-representations of quivers and related polynomial semi-invariants
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-19
    V. A. Bovdi; A. N. Zubkov

    We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.

    更新日期:2020-02-19
  • The free spectrum of A5
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-11
    William Cocke; Dane Skabelund

    We obtain a formula for the orders of the relatively free groups of finite rank in the variety generated by the alternating group A5. This is accomplished by explicitly determining the structure of the commutator subgroups of these groups.

    更新日期:2020-02-11
  • Superalgebras with superinvolution or graded involution with colengths sequence bounded by 3
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-11
    Antonio Ioppolo

    Let A be a superalgebra with superinvolution or graded involution over a field of characteristic zero and let χn1,…,n4(A), n1+⋯+n4=n, be the (n1,…,n4)-cocharacter of A. The ∗-colengths sequence, ln∗(A), n=1,2,…, is the sum of the multiplicities in the decomposition of the (n1,…,n4)-cocharacter χn1,…,n4(A), for all n=n1+⋯+n4≥1. The main purpose of this paper is to classify the superalgebras with superinvolution

    更新日期:2020-02-11
  • Hausdorff series in a semigroup ring
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-11
    Şehmus Fındık; Osman Kelekci̇

    Let A=ℝ〈a1,…,an〉 and B=ℝ〈b1,…,bn〉 be the semigroup rings spanned on the right zero semigroup RZn={a1,…,an}, and on the left zero semigroup LZn={b1,…,bn}, respectively, together with the identity element 1. We suggest a closed formula solving the equation w=log(euev) which is the evolution of the Campbell–Baker–Hausdorff formula given by the Hausdorff series w=H(u,v)=u+v+12[u,v]+112[u,[u,v]]+112[v,[v

    更新日期:2020-02-11
  • Solutions to twisted word equations and equations in virtually free groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-02-03
    Volker Diekert; Murray Elder

    It is well known that the problem solving equations in virtually free groups can be reduced to the problem of solving twisted word equations with regular constraints over free monoids with involution. In this paper, we prove that the set of all solutions of a twisted word equation is an EDT0L language whose specification can be computed in PSPACE. Within the same complexity bound we can decide whether

    更新日期:2020-02-03
  • Bounded homomorphisms and finitely generated fiber products of lattices
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-01-28
    William DeMeo; Peter Mayr; Nik Ruškuc

    We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto lattices satisfying a property we call Dean’s condition (D) which arises from Dean’s solution to the word problem for finitely presented lattices. In particular, all finitely presented lattices and those satisfying Whitman’s condition satisfy (D). For lattice

    更新日期:2020-01-28
  • Distributive biracks and solutions of the Yang–Baxter equation
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-01-21
    Přemysl Jedlička; Agata Pilitowska; Anna Zamojska-Dzienio

    We investigate a class of non-involutive solutions of the Yang–Baxter equation which generalize derived (self-distributive) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang–Baxter (permutation) groups of such solutions are nilpotent. We formulate the results in the language of biracks which allows us to apply universal algebra tools.

    更新日期:2020-01-21
  • Relations in the semigroup of 2 × 2 upper-triangular matrices
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-01-15
    Henri-Alex Esbelin; Marin Gutan

    Let M,N1,N2,…,Nt+1, with t∈N∗, be 2×2 upper-triangular matrices with rational entries. In the multiplicative semigroup generated by these matrices, we check if there are relations of the form N1Mn1N2Mn2⋯MntNt+1=N1Mm1N2Mm2⋯MmtNt+1, where n=(n1,…,nt)∈Nt,m=(m1,…,mt)∈Nt and n≠m. We give algorithms to find relations of the previous form. Our results are extensions of some theorems obtained by Charlier and

    更新日期:2020-01-15
  • Growth in Baumslag–Solitar groups II: The Bass–Serre tree
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-01-14
    Jared Adams; Eric M. Freden

    Denote the Baumslag–Solitar family of groups as BS(p,q). When p|q we study the Bass–Serre tree 𝒯 for BS(p,q) as a geometric object. We suggest that the irregularity of 𝒯 is the principal obstruction for computing the growth series for the group. In the particular case p=2,q=4 we exhibit a set ℒ of normal form words having minimal length for 𝒯 and use it to derive various counting algorithms. The

    更新日期:2020-01-14
  • Product rules and classification of nonassociative Moufang loops of order 81
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-01-09
    Wing Loon Chee; Andrew Rajah

    In this paper, we produce the product rules of nonassociative Moufang loops of order 81 by using an analytical approach. We then explore all possible presentations on a suitable set of generators, thereby obtaining a total of five nonisomorphic cases. The result is in agreement with the classification by Nagy and Vojtěchovský using the GAP package LOOPS.

    更新日期:2020-01-09
  • Realizable ranks of joins and intersections of subgroups in free groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-12-09
    Ignat Soroko

    The famous Hanna Neumann Conjecture (now the Friedman–Mineyev theorem) gives an upper bound for the ranks of the intersection of arbitrary subgroups H and K of a non-abelian free group. It is an interesting question to “quantify” this bound with respect to the rank of H∨K, the subgroup generated by H and K. We describe a set of realizable values (rk(H∨K),rk(H∩K)) for arbitrary H, K, and conjecture

    更新日期:2019-12-09
  • The complexity of properties of transformation semigroups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-12-06
    Lukas Fleischer; Trevor Jack

    We investigate the computational complexity for determining various properties of a finite transformation semigroup given by generators. We introduce a simple framework to describe transformation semigroup properties that are decidable in AC0. This framework is then used to show that the problems of deciding whether a transformation semigroup is a group, commutative or a semilattice are in AC0. Deciding

    更新日期:2019-12-06
  • The complexity of the equation solvability and equivalence problems over finite groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-12-04
    Attila Földvári; Gábor Horváth

    We provide a polynomial time algorithm for deciding the equation solvability problem over finite groups that are semidirect products of a p-group and an Abelian group. As a consequence, we obtain a polynomial time algorithm for deciding the equivalence problem over semidirect products of a finite nilpotent group and a finite Abelian group. The key ingredient of the proof is to represent group expressions

    更新日期:2019-12-04
  • Decompositions of algebras and post-associative algebra structures
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-12-02
    Dietrich Burde; Vsevolod Gubarev

    We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota–Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such structures. In particular, we prove that there exists no post-Lie algebra structure on a pair (𝔤,𝔫), where 𝔫 is a simple Lie algebra and 𝔤 is a reductive Lie

    更新日期:2019-12-02
  • Loop conditions for strongly connected digraphs
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-12-02
    Miroslav Olšák

    We prove that every strongly connected (not necessarily finite) digraph of algebraic length 1, which is compatible with an operation t satisfying a non-trivial identity of the form t(…)≈t(…), has a loop.

    更新日期:2019-12-02
  • A criterion for Kolchin subgroups of Out(Fr)
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-29
    Edgar A. Bering IV

    This paper provides a decidable criterion for when a subgroup of Out(Fr) generated by two Dehn twists consists entirely of polynomially growing elements, answering an earlier question of the author.

    更新日期:2019-11-29
  • Matrix semigroups over semirings
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-26
    Victoria Gould; Marianne Johnson; Munazza Naz

    We study properties determined by idempotents in the following families of matrix semigroups over a semiring S: the full matrix semigroup Mn(S), the semigroup UTn(S) consisting of upper triangular matrices, and the semigroup Un(S) consisting of all unitriangular matrices. Il’in has shown that (for n>2) the semigroup Mn(S) is regular if and only if S is a regular ring. We show that UTn(S) is regular

    更新日期:2019-11-26
  • Multiplier Hopf algebras: Globalization for partial actions
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-26
    Graziela Fonseca; Eneilson Fontes; Grasiela Martini

    In partial action theory, a pertinent question is whenever given a partial action of a Hopf algebra A on an algebra R, it is possible to construct an enveloping action. The authors Alves and Batista, in [M. Alves and E. Batista, Globalization theorems for partial Hopf (co)actions and some of their applications, groups, algebra and applications, Contemp. Math.537 (2011) 13–30], have shown that this

    更新日期:2019-11-26
  • Boundary dynamics for bireversible and for contracting automaton groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-25
    Daniele D’Angeli; Thibault Godin; Ines Klimann; Matthieu Picantin; Emanuele Rodaro

    We study the dynamics of the action of an automaton group on the set of infinite words, and more precisely the discontinuous points of the map which associates to a point its set of stabilizers — the singular points. We show that, for any Mealy automaton, the set of singular points has measure zero. Then we focus our attention on several classes of automata. We characterize those contracting automata

    更新日期:2019-11-25
  • The relative hyperbolicity and manifold structure of certain right-angled Coxeter groups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-25
    Matthew Haulmark; Hoang Thanh Nguyen; Hung Cong Tran

    In this paper, we study the manifold structure and the relative hyperbolic structure of right-angled Coxeter groups with planar nerves. We then apply our results to the quasi-isometry problem for this class of right-angled Coxeter groups.

    更新日期:2019-11-25
  • Multiplicative factorization in numerical semigroups
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2019-11-18
    Nicholas R. Baeth; Matthew Enlow

    A numerical semigroup is a nonempty additively closed subset S⊆ℕ0 with |ℕ0\S|<∞. The arithmetic, that is the additive factorization properties, of numerical semigroups has been well studied. Their multiplicative properties, on the other hand, have received little, if any, attention. If S=ℕ or S=ℕ\{1}, then multiplicative factorization (as products of primes) in S is unique. However, if there is n>1

    更新日期:2019-11-18
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