Hopf代数的二重Ore扩张

本文的目的是定义Hopf二重Ore扩张,讨论这种扩张的基本性质并研究Hopf 代数的分次与Hopf二重Ore扩张之间的关系.作者还研究了连通分次Hopf代数的结构及其Hopf二重Ore扩张的同调性质.     

On standard integral table algebras generated by an element of width 2

The paper studies standard integral table algebras containing an element of width two. It is shown that the table subalgebra generated by such an element is exactly isomorphic to one of the table algebras described in Main Theorems 1.1. and 1.2. The contribution of this author is a part of his Ph.D. thesis at Bar-Ilan University under the supervision of Z. Arad and M. Muzychuk. This author was partially supported by the Israeli Ministry of Absorption.     

On identities for coalgebras and hopf algebras

The notion of a polynomial identity for algebras is well-known. In this work the notion of identity is transferred to coalgebras (where one may call it a coidentity). The author studies the basic properties of coidenti-ties, some examples of Hopf algebras with an identity or a coidentity are considered.     

Embedding of Lie Algebras in Isogeneralized Structurable Algebras

In a previous paper, the first-named author introduced generalized structurable algebras, while the second-named author introduced the isotopies of Lie algebras. In this paper, we combine the two analyses, submit the notion of isogeneralized structural algebras, and show that they include Lie algebras, all their axiom-preserving generalizations of graded, supersymmetric or isotopic type, as well as numerous other algebras.     

The free product of algebras with standard base for ideals

A wide class of associative algebras admitting standard bases of ideals was introduced in previous papers of the author. They are referred to as algebras with strong filtration. This class includes all known examples of associative algebras whose ideals possess standard bases. It was proved by the author that the class of algebras with strong filtration is closed with respect to direct sums and tensorial products. In this paper it is shown that this class is also closed with respect to free products of algebras.     

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…     

Solvable quadratic Lie algebras

A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.     

Group-Like Algebras and Their Representations

The concept of “group-like algebras” was defined by the author as a special class of bF algebras. They generalize scheme rings (Bose–Mesner algebras) of noncommutative association schemes. We develop the representation theory for group-like algebras and symmetric bF algebras. We also study group-like algebras of association-scheme type with dimension 2 and 3.     

偏代数族的积偏代数

定义了一族偏代数物积偏代数的概念，且对偏代数间的同态映射，由同态映射诱导的合同关系及由同态映射和合同关系诱导的合同关系与积偏代数一起作了深入的讨论，分别得到了一些有意义的结果。     

On Complete Lie Algebras

In this article, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.     

同余可换的Stone代数

借助Stone代数的对偶空间的性质，考察了Stone代数的同余可换性.     

Recognition of certain properties of automaton algebras

Abstract. The paper considers a new algebraic object, the completely automaton binomial algebras, which generalize certain existing classes of algebras. The author presents a classification of semigroup algebras taking into account completely automaton algebras and gives the corresponding examples. A number of standard algorithmic problems are solved for completely automaton binomial algebras: the recognition of a strict and nonstrict polynomial property, the recognition of the right and/or left finite processing, and the construction of the determining regular language for an algebra with finite processing and for monomial subalgebras of a free associative algebra and certain completely automaton algebras. For an automaton monomial algebra, the author constructs the left syzygy module of a finite system of elements and the Gröbner basis of a finitely generated left ideal; also, some algorithmic problems are solved.     

Braided symmetric and exterior algebras and quantizations of braided lie algebras

We study quantizations of braided symmetric and exterior algebras of graded vector spaces and of braided derivations on these algebras. We find quantizations of braided Lie algebras by considering quantizations of derivations on their braided exterior algebra. The text was submitted by the author in English.     

广义矩阵代数上的李导子

研究了广义矩阵代数上的一类李导子,证明了广义矩阵代数上李导子可以表示成一个导子和一个中心映射之和,并将这个结果应用到全矩阵代数上.     

Isomorphisms Between Quasi-Banach Algebras

In this paper, the author proves the Hyers-Ulam-Rassias stability of homo-morphisms in quasi-Banach algebras. This is used to investigate isomorphisms between quasi-Banach algebras.     

Morphisms of double frobenius algebras. i

Double Frobenius algebras (or dF-algebras) were recently introduced by the author. The concept includes finite-dimensional Hopf algebras, adjacency algebras of (non-commutative) association schemes, and C-algebras (character algebras). In this paper we define certain kinds of morphisms of dF-algebras and develop their basic theory. The morphisms generalize homomorphisms of Hopf algebras and of C-algebras.     

Classifying pointed hopf algebras of dimension 16

We classify pointed Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. Apart from the 11 group algebras, there are 29 such Hopf algebras. All of them can be obtained using the Ore extension construction, as described recently by Beattie, the second author, and Grunenfelder.     

Constructing cell data for diagram algebras

We show how the treatment of cellularity in families of algebras arising from diagram calculi, such as Jones’ Temperley-Lieb wreaths, variants on Brauer’s centralizer algebras, and the contour algebras of Cox et al. (of which many algebras are special cases), may be unified using the theory of tabular algebras. This improves an earlier result of the first author (whose hypotheses covered only the Brauer algebra from among these families).     

The centers of generic division algebras with involution

The main goal of this paper is a study of the centers of the generic central simple algebras with involution. These centers are shown to be invariant fields under finite groups in a way analagous to the center of the generic division algebras. The centers of the generic central simple algebras with involution are also described as generic splitting fields (i.e. function fields of Brauer-Severi varieties) over the centers of generic division algebras. Finally, a generic central simple algebra is described for the class of central simple algebras with subfields of a certain dimension. The first author would like to thank the Department of Mathematics of The University of Texas at Austin for its hospitality and the NSF for its support under grant DMS 585-05767. The second author would like to thank the NSF for its support under grants DMS 8303356 and DMS 8601279.