相关论文: Associativity, Jacobi, Bremner, and All That

In this paper, the definitions of algebras of quotients and Martandale-like qoutients of Leibniz algebras are introduced and the interactions between the two quotients are determined. Firstly, some important properties which not only hold…

Algebraic relations that characterize quantum statistics (Bose-Einstein statistic, Fermi-Dirac statistic, supersymmetry, parastatistic, anyonic statistic, ...) are reformulated herein in terms of a new algebraic structure, which we call…

The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.

In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs and several results seem to be new.

We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras

A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.

The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bialgebras and Hopf algebras and investigate their properties.…

In this paper we study the categories of braided categorical associative algebras and braided crossed modules of associative algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed…

In this paper I consider the structure of the polylinear mapping of the free algebra over the commutative ring.

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…

We introduce higher-order (or multibracket) simple Lie algebras that generalize the ordinary Lie algebras. Their `structure constants' are given by Lie algebra cohomology cocycles which, by virtue of being such, satisfy a suitable…

The representation and the cohomology theory of associative 2-algebras are developed. We study the deformations and abelian extensions of associative 2-algebras in details.

The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…

The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.

The paper presents two new results concerning the varieties of Leibnitz algebras. We find values of multiplicities and colength variety of Leibniz algebras of almost polynomial growth, which is generated by the algebra constructed with the…

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…

We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.

Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…