Betti numbers for p -stable ideals

Abstract

All Riemannian algebras of dimension ≤3 are classified in this paper.     

Standardly Stratified Extension Algebras

Abstract

The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution – the so called linearly stratified algebras – is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincaré series of the corresponding modules.

     

Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras

Abstract

In this paper, all one-dimensional Leibniz central extensions on the algebras of differential operators over C[t, t ^?1] and C((t)), as well as on the quantum 2-torus, the Virasoro-like algebra and its q-analog are studied. We determine all nontrivial Leibniz 2-cocycles on these infinite dimensional Lie algebras.     

Complexity of gauge bounded Cartier algebras

Abstract

We show that a gauge bounded Cartier algebra has finite complexity. We also give an example showing that the converse does not hold in general.

Communicated by Graham J. Leuschke     

Commutative Algebras with Radical Cube Zero

Abstract

We present “canonical forms” of finite dimensional (quasi-Frobenius) commutative algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. We also determine the isomorphism classes of the algebras Λ over some typical fields.     

Leibniz algebras constructed by Witt algebras

ABSTRACT

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself.     

Notes on Hilbert-Kunz Multiplicity of Rees Algebras

Abstract

In this paper, we estimate the Hilbert-Kunz multiplicity of the (extended) Rees algebras in terms of some invariants of the base ring. Also, we give an explicit formula for the Hilbert-Kunz multiplicities of Rees algebras over Veronese subrings.     

A Generalization of Lazard's Elimination Theorem

Abstract

Using the classical Lazard's elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type.     

On Restricted Leibniz Algebras

ABSTRACT

The role played by fields in relation to Galois Rings corresponds to semifields if the associativity is dropped, that is, if we consider Generalized Galois Rings instead of (associative) Galois rings. If S is a Galois ring and pS is the set of zero divisors in S, S* = S\ pS is known to be a finite {multiplicative} Abelian group that is cyclic if, and only if, S is a finite field, or S = ?/n? with n = 4 or n = p ^r for some odd prime p. Without associativity, S* is not a group, but a loop. The question of when this loop can be generated by a single element is addressed in this article.     

The Partition Algebra as a Centralizer Algebra of the Alternating Group

ABSTRACT

In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra.     

Quasi L 3 -Filiform Lie Algebras

Abstract

In this paper, we mainly discuss some properties of quasi L ₃-filiform Lie algebras and their derivation algebras.     

The deformed twisted Heisenberg–Virasoro type Lie bialgebra

Abstract

In this article, we investigate Lie bialgebra structures on the deformed twisted Heisenberg–Virasoro Lie algebra. Sufficient and necessary conditions for this type Lie bialgebra structures to be triangular coboundary are given.

Communicated by K. C. Misra     

The Ascending Tree Condition: Constructive Algebra Without Countable Choice

Abstract

A strengthening of the ascending chain condition allows a choice-free constructive development of the theory of Noetherian modules. Related topics in the theory of PID's and elementary divisor rings are also explored.     

The Lie Module Function for Symmetric Groups #

Let V be a ? G-module where ? is the field of all complex numbers and G is a symmetric group. The purpose of this article is to give a method of analyzing the Lie powers L ⁿ (V ), for every positive integer n, by making use of the recent work of Bryant.     

-QUASIALGEBRAS

Abstract

The purpose of this work is to construct completely reducible vertex representations for the toroidal Lie algebra of type F ₄.     

Quantum Yang-Baxter H-Module Algebras and Their Braided Products

Abstract

We give a necessary and sufficient condition of the braided product to be a bialgebra or a Hopf algebra and two interesting examples to show that the conditions in Theorem 2.4: “(H1) and (H2)” weaken the commutativity and cocommutativity of H in Caenepeel et al. (Caenepeel, S., Oystaeyen, F. Van, Zhang, Yin-huo (1994). Quantum Yang-Baxter module algebra. K-Theorem 8:231–255.). Dually, we introduce the concept of a braided coproduct and give the distinguished conditions.     

Prime Ideals of Cancellative Semigroups

Abstract

For a class of prime ideals P of a cancellative semigroup S it is shown that the factors S/P have a structure of a monomial semigroup over a group. Consequences for the semigroup algebras K[S] are discussed.     

The Endomorphism Kernel Property in Finite Distributive Lattices and de Morgan Algebras

Abstract

An algebra 𝒜 has the endomorphism kernel property if every congruence on 𝒜 different from the universal congruence is the kernel of an endomorphism on 𝒜. We first consider this property when 𝒜 is a finite distributive lattice, and show that it holds if and only if 𝒜 is a cartesian product of chains. We then consider the case where 𝒜 is an Ockham algebra, and describe in particular the structure of the finite de Morgan algebras that have this property.     

An Equivalence of Categories for Lie Color Algebras

Abstract

Let k be a field with char k = p > 0 and G an abelian group with a bicharacter λ on G. For each p-(G,λ)-Lie color algebra L over k the p-universal enveloping algebra u(L) is a G-graded Hopf algebra,i.e.,a Hopf algebra in the category ^kG ? of kG-comodules. In this paper we describe a subcategory of ^kG ? which is equivalent to the category of the finite dimensional p-(G,λ)-Lie color algebras over k.