Showing papers in "Communications in Algebra in 1995"
TL;DR: In this paper, Strongly homotopy lie algebras have been studied in the context of algebraic graph theory, and they are shown to be strongly homotopomorphic.
Abstract: (1995). Strongly homotopy lie algebras. Communications in Algebra: Vol. 23, No. 6, pp. 2147-2161.
576 citations
TL;DR: In this article, a characterisation of hilbert spaces by orthomodular spaces is presented. But this characterization is restricted to the case of orthomorphism and it is not applicable to the HILBERT space.
Abstract: (1995). Characterization of hilbert spaces by orthomodular spaces. Communications in Algebra: Vol. 23, No. 1, pp. 219-243.
222 citations
TL;DR: In this paper, the authors express the presentation ideal of R(I), the Rees algebra of I, in terms of the syzygies of I and its edge ideal.
Abstract: Let G be a graph and let I be its edge ideal. We express the presentation ideal of R(I), the Rees algebra of I, in terms of the syzygies of I and the presentation ideal of the special fiber of R(I). A description of the elementary integral vectors of the kernel of the incidence matrix of G is given and then used to study the special fiber of R(I) via Grobner bases.
201 citations
TL;DR: In this article, the twisted tensor products of algebras are studied and the authors propose an approach to solve the problem of tensor product decomposition in the context of algebraic geometry.
Abstract: (1995). On twisted tensor products of algebras. Communications in Algebra: Vol. 23, No. 12, pp. 4701-4735.
180 citations
TL;DR: A "Practical" algorithm to construct random elements of a finite group is presented and it is proved that asymptotically it produces uniformly distributed tuples of elements.
Abstract: We present a "Practical" algorithm to construct random elements of a finite group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed tuples of elements. We discuss tests to assess its effectiveness and use these to decide when its results are acceptable for some matrix groups.
165 citations
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124 citations
TL;DR: In this paper, the authors studied the cohomology of the graded F -algebra A = A(A) = ⊕p=0Ap generated by the differential forms ωi = dαi/αi ∈ A1.
Abstract: Let V be an affine space of dimension ` over a field F and let A = {H1, H2, . . . , Hn} be a non-empty arrangement of hyperplanes of V . For each H ∈ A fix an affine functional αH such that kerαH = H and put αi = αHi . The main character of the paper is the graded F -algebra A = A(A) = ⊕p=0Ap generated by the differential forms ωi = dαi/αi ∈ A1. If F = C then, according to Brieskorn’s theorem [2], this algebra is isomorphic under the de Rham map to the cohomology algebra of M = V \\ ⋃ni=1Hi. Explicit and pure combinatorial description of this algebra has been given by Orlik and Solomon [6] and is presented in detail in Section 3 of [7]. For every λ = (λ1, . . . , λn) ∈ F n the left multiplication dλ by ωλ = ∑n i=1 λiωi defines a cochain complex (A, dλ) 0 → A0 dλ → A1 dλ → · · · dλ → A` → 0. The goal of this paper is to study the cohomology H = H(A, dλ) of this complex. The study of H is motivated by [4] and [5]. These papers are concerned with H∗(M,L) for F = C where L is a local system on M . The cohomology is used in theory of hypergeometric functions and Knizhnik-Zamolodchikov equations. Kohno [5] proved that if L is the local system of flat sections of the trivial bundle with respect to the connection d+ωλ, then under a certain genericity condition on λ, H(M,L) = 0 for p < `. Also if A is real and transverse to the hyperplane at infinity, he found a basis of H(M,L) that does not depend on λ. Then Esnault, Schechtman, and Viehweg [4] proved that under a weaker genericity condition on λ
96 citations
TL;DR: In this article, the isomorphic classes of 6 or 8 dimensional semisimple Hopf algebras over an algebraically closed field such that (dimA)1≠0.
Abstract: We determine the isomorphic classes of 6 or 8 dimensional semisimple Hopf algebrasA over an algebraically closed field such that (dimA)1≠0.
72 citations
TL;DR: In this article, a combinatorial rule to compute the composition of two convolution products of endomorphisms of a free associative algebra and deduce the construction of a subalgebra of QB n is given.
Abstract: In this paper we give a combinatorial rule to compute the composition of two convolution products of endomorphisms of a free associative algebra and deduce the construction of a subalgebra of QB n ...
66 citations
TL;DR: In this paper, it was shown that every Harish-Chandra module over the super-Virasoro algebras is either a highest or lowest weight module, or a module of the intermediate series.
Abstract: In this paper, we first construct all indecomposable modules whose dimensions of weight spaces of the even and odd parts are ≤ 1, then classify all Harish-Chandra module over the super-Virasoro algebras, proving that every Harish-Chandra module over the super-Virasoro algebras is either a highest or lowest weight module, or else a module of the intermediate series. This result generalizes a theorem which was originally given as a conjecture by Kac on the Virasoro algebra.
TL;DR: In this paper, it was shown that if R is semiprime with suitably-restricted additive torsion, then R must contain nonzero central ideals if one of the following holds: (i) [x, [x n, D(x)], ∊ Z for all x ∊ U; (ii) for a fixed positive integer n, [n, D n, X n, Y n] ∊ X for all X ∊ Y ∊ N;
Abstract: Let R be a ring, Z its center, U a nonzero left ideal, and D:R → R a derivation. We show that if R is semiprime with suitably-restricted additive torsion, then R must contain nonzero central ideals if one of the following holds: (i) [x, [x, D(x)]] ∊ Z for all x ∊ U; (ii) for a fixed positive integer n, [xn, D(x)] ∊ Z for all x ∊ U
TL;DR: The hall polynomials of a cyclic serial algebra have been studied in this paper for the first time in the context of algebraic serial algebras, and they are shown to be polynomial in the following classes:
Abstract: (1995). The hall polynomials of a cyclic serial algebra. Communications in Algebra: Vol. 23, No. 2, pp. 743-751.
TL;DR: In this paper, it was shown that the Hilbert function of a GSA has local maxima at any given set of points with the symmetry and the socle degree as the only restrictions.
Abstract: In [4] Stanley showed that the Hilbert function of graded Goren-stein Artin algebras need not be unimodal. In this article we prove the exis¬tence of graded Gorenstein Artin algebras whose Hilbert functions have local maxima at any given set of points with the symmetry and the socle degree as the only restrictions.
TL;DR: In this article, simple GP - injective modules are discussed and a simple GP-based injective module for simple GP is proposed. Communications in Algebra: Vol. 23, No. 14, pp. 5437-5444.
Abstract: (1995). On simple GP - injective modules. Communications in Algebra: Vol. 23, No. 14, pp. 5437-5444.
TL;DR: In this paper, a 3-parameter family of deformations of U(S12) is introduced and the finite dimensional simple representations are studied using non-commutative projective geometry.
Abstract: A 3-parameter family of deformations of U(S12) is introduced. The finite dimensional simple representations are studied using non-commutative projective geometry.
TL;DR: A generalization of macaulay's theorem has been proposed in this paper, where the authors propose a generalization to the problem of algebraic generalizations of Macaulay theorem.
Abstract: (1995). A generalization of macaulay's theorem. Communications in Algebra: Vol. 23, No. 4, pp. 1249-1263.
TL;DR: In this article, an anti-homomorphic image of the automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group.
Abstract: The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq
TL;DR: In this article, the minimal number of generators of finite non-abelian p-groups having an abelian automorphism group is studied, where the generator is defined as a generator of a p-group having an automomorphism group.
Abstract: (1995). On the minimal number of generators of finite non-abelian p-groups having an abelian automorphism group. Communications in Algebra: Vol. 23, No. 6, pp. 2045-2065.
TL;DR: In this paper, a map f : A→R is commuting on A if [f(x),x]= 0 for all xeA where [x,y] = xy − yx.
Abstract: Let R be a ring and let A be a subset of R. A map f : A→ R is commuting on A if [f(x),x]= 0 for all xeA where [x,y] = xy — yx. Suppose that R is a prime ring of characteristic ≠2 with extended centroid C. If L is a noncommutative Lie ideal of R and f:L→R an additive commuting map, then there is λe C and an additive map ∈: L→ C such that f(v) = λ(v)=λv+∈((v) for all veL.
TL;DR: In this article, the Stanley-reisner rings with pure resolutions are described and compared to the pure-resolve rings with a pure-resolution ring with pure resolution (PSR).
Abstract: (1995). Stanley-reisner rings with pure resolutions. Communications in Algebra: Vol. 23, No. 4, pp. 1201-1217.
TL;DR: In this article, the authors give conditions on the action of the group in order to make the skew group ring an Azumaya algebra, which is a special case of twisted group rings.
Abstract: If S is a ring with 1, and G is a finite group acting faithfully as automorphisms of S, then it is well known that the skew group ring S ∗ G is a separable extension of S if and only if there exists a central element in S with trace one. A ring is an Azumaya algebra if it is separable over its center. The case of when the group ring S[G] is Azumaya was studied by De Meyer and Janusz in [2] ; and lately the case of twisted group rings was studied by Szeto and Wong in [5] ; but the techniques used on those cases cannot be applied to the skew group rings precisely because the elements of the ring S do not commute with the elements of the group G. The purpose of this paper is to give conditions on the action of the group in order to make the skew group ring an Azumaya algebra. A ring A is said to be separable over a subring B if the (A − A)-module homomorphism of A⊗BA onto A defined by a⊗b 7−→ ab splits, and A is called H-separable over B if A ⊗B A is isomorphic as (A − A)-bimodule to a direct summand of A for some n ≥ 1. Clearly H-separable extension are separable. Let S be a ring with 1 and G be a finite group acting as automorphisms of S with fixed ring S; that we will denote R. The skew group ring S ∗G is the free left S-module with basis G, where multiplication is defined according
TL;DR: Some honey-combs in hyperbolic 3-space have been studied in this paper, where the authors show how to construct a honeycomb in the 3-dimensional space.
Abstract: (1995). Some honey-combs in hyperbolic 3-space. Communications in Algebra: Vol. 23, No. 14, pp. 5169-5206.
TL;DR: In this article, the authors classify the primitive multiplicity-free representations of the sporadic simple groups and their automorphism groups and determine all the distance-transitive graphs arising from these representations.
Abstract: A permutation representation of a finite group is multiplicity-free if all the irreducible constituents in the permutation character are distinct. There are three main reasons why these representations are interesting: it has been checked that all finite simple groups have such permutation representations, these are often of geometric interest, and the actions on vertices of distance-transitive graphs are multiplicity-free. In this paper we classify the primitive multiplicity-free representations of the sporadic simple groups and their automorphism groups. We determine all the distance-transitive graphs arising from these representations. Moreover, we obtain intersection matrices for most of these actions, which are of further interest and should be useful in future investigations of the sporadic simple groups.