Showing papers in "Journal of Algebra in 2003"

TL;DR: In this article, it was shown that for a large class of finitely generated groups the classical decision problems of group theory (the word, conjugacy, and membership problems) all have linear-time generic-case complexity.

TL;DR: In this article, it was shown that every height-three complete intersection has the weak or strong Lefschetz property, and a sharp bound on the graded Betti numbers of K-algebras with the weak and strong lefscheckz property and fixed Hilbert functions was given.

TL;DR: In this paper, it was shown that if R is a local commutative ring with at least 33 elements, and Γ ( R )≠∅, then Γ( R ) is not planar.

TL;DR: In this article, a graded version of category O is considered and a graded translation functors and duality is defined. But the results of these papers are different from those of [Beilinson et al., J. Math. Soc. 9 (1996) 473-527] using a different approach.

TL;DR: In this article, it was shown that α(x) n is the minimal numbe of L-conjugates of x which generate the group 〈L,x〉.

TL;DR: In this article, Carriere and Ghys gave an elementary proof to a conjecture of Connes and Sullivan on amenable actions, which was first proved by Zimmer in the context of real Lie groups.

TL;DR: Cauchon et al. as discussed by the authors constructed the derivative-elimination algorithm, which consists of a sequence of changes of variables inside the division ring F=Fract(R), starting with the indeterminates (X1, X2, XN) and terminating with new variables (T1, T1, N) to generate some quantum-affine space R such that F= Fract(R ).

TL;DR: In this article, a faster algorithm for solving the conjugacy problem in Artin braid groups was presented, which is faster than the one presented by Birman, Ko, and Lee [Adv. Math. 139 (1998) 322-353].

TL;DR: In this article, the authors investigated the degree of the closed image of a rational map given by some homogeneous elements of the same degree in a graded algebra and proved new acyclicity criteria for the associated approximation complexes.

TL;DR: In this paper, the cyclic sum identities of multiple zeta values were established, which imply the sum theorem for multiple zetas, and they also have a succinct statement in terms of cyclic derivations.

TL;DR: In this article, the number of pairwise nonisomorphic commutative semifield planes of even order N obtained in this manner was not bounded above by any polynomial in N.

TL;DR: In this paper, the authors investigate the class of piecewise prime, PWP, rings which properly includes all piecewise domains (hence all right hereditary rings which are semiprimary or right Noetherian), and determine a large class of ring extensions which have a generalized triangular matrix representation for which the diagonal rings are prime.

TL;DR: In this article, the authors studied the representation theory of the algebraic supergroup Q(n) in positive characteristic, motivated by its close relationship to the double covers of the symmetric groups.

TL;DR: Kawanaka et al. as mentioned in this paper gave a conceptual proof of Pommerening's theorem, which states that any nilpotent element in Image is Richardson in a distinguished parabolic subalgebra of the Lie algebra of a Levi subgroup of G.

TL;DR: In this article, the set A n (A,V) of all representatives of isomorphism classes of Frobenius algebras Γ with the properties (1) Γ /rad Γ ≅ A, (2) A ( rad Γ/ rad 2 Γ) A ≅V, and (3) ǫ n Γ = 0 is investigated.

TL;DR: In this article, the authors classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators and show that these correspond to the W(2,2p−1)-algesas with central charge 1−6(p −1)2/p where p is a positive integer, p⩾2.

TL;DR: In this paper, it was shown that the (PSI) condition on a ring is left-right asymmetric, i.e., every factor ring modulo the right annihilator of a principal right ideal is 2-primal.

TL;DR: GoodGoodearl-Letzter H-stratification of Spec(R) as mentioned in this paper is a natural embedding ϕ : Spec (R)→ Spec ( R ) and asserts that the canonical image ϕ(Spec(R)) is a union of strata Spec w ( R ), where w describes some subset W of P (〚1,n〛 2 ).

TL;DR: In this article, it was shown that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf algebra D ω ( Σ ), for some finite group Σ and some ω ∈ Z 3 ∈ k ×.

TL;DR: In this paper, the concept of crown was employed to study the generalized Euler factors of the probabilistic zeta function of finite groups, and they employed crown to analyze the generalized generalized euler factors for finite groups.

TL;DR: In this paper, a combinatorial property of positive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation.

TL;DR: In this article, the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics are described.

TL;DR: Weakly Koszul modules have been studied in this article, where it is shown that if the Koskul dual of a finite-dimensional Koszula algebra is Noetherian, then every finitely generated graded module has a weakly-koszul syzygy and as a consequence a rational Poincare series.

TL;DR: In this paper, the authors introduce the notion of endomorphic presentations, which are group presentations whose relations are iterated under a set of substitutions on the generating set, and show that a broad class of groups acting on rooted trees admit explicitly constructible finite L-presentations.

TL;DR: In this paper, the problem of classification of infinite subalgebras of CendN and of gcN that acts irreducibly on C[∂]N is discussed.

TL;DR: In this article, the structure of two classes of modules called pseudo Cohen-Macaulay and pseudo generalized Cohen-macaulay modules is studied and a characterization for these modules in terms of the Cohen and Macaulayness is given.

TL;DR: The irreducible calibrated representations for affine Hecke algebras have been studied in this paper, where the indexing sets for weight spaces are generalizations of standard Young tableaux.