相关论文: Associativity, Jacobi, Bremner, and All That
In this paper we explore a new method of analysis of associative algebras.
We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…
Adjoint functors between the categories of crossed modules of dialgebras and Leibniz algebras are constructed. The well-known relations between the categories of Lie, Leibniz, associative algebras and dialgebras are extended to the…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
We extend the concepts of the associator and commutator from algebras with a binary multiplication law to algebras with a ternary multiplication law using cube roots of unity. By analogy with the Jacobi identity for the binary commutator,…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized…
The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…
A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…
In this paper, we consider four types of subvarieties of the variety of associative algebras. We study these subvarieties from the point of view of operads and show their connections with well-known classes of algebras, such as dendriform…
The Jacobian algebras are introduced and their various properties are studied.
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
Generalizing work of Marin [12], we construct in a unified way all the "braids and ties'' algebras available in literature and new ones.
A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation for a Leibniz algebra in order to realize the abstract…
We study the Frattini subalgebra of Leibniz algebras generated by one element. We also investigate Leibniz algebras all of whose proper subalgebras are elementary.