Related papers: Isoclinism of Algebras With Bracket
In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.
The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…
Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in…
The purpose of this paper is to explore possible definitions of $n$-isoclinism for skew braces. We also introduce the notions of verbal sub-skew braces and marginal left ideals.
The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…
We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…
The aim of this article is to advance the knowledge on the theory of skew left braces. We introduce a subclass of skew left braces, which we denote by $\mathcal{I}_n$, $n \ge 1$, such that elements of the annihilator and lower central…
In this paper we introduce the concept of $n$-Lie-isoclinism on non-Lie Leibniz algebras. Among the results obtained, we provide several characterizations of $n$-Lie-isoclinic classes of Leibniz algebras. Also, we provide a characterization…
We introduce an analogue of the famous Schur multiplier in the context of associative trialgebras, or triassociative algebras. The latter were first studied by Loday and Ronco in 2001, and are characterized by three operations and eleven…
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
We give two sufficient and necessary conditions for a Hochschild extension of a finite dimensional algebra by its dual bimodule and a Hochschild 2-cocycle to be a symmetric algebra.
For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant…
Many theorems and formulas of Lie algebras run quite parallel to Lie superalgebra case, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case, as these…
We define and study a new class of bialgebras, which generalize certain Turner double algebras related to generic blocks of symmetric groups. Bases and generators of these algebras are given. We investigate when the algebras are symmetric,…
We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Relying on the proof of…
We consider the algebraization problem for principal bundles with reductive structure group, defined on the complement of a closed subset Z in a proper formal scheme. We show that, when Z is of codimension at least 3, an algebraization…
Similar to works of G. Ellis (1998), the concept of covering pair of Lie algebras is defined. Also, we show the existence of covering pair for the pair of Lie algebras (L,N) and then show that every crossed module is a homomorphic image of…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattice gauge field theory.
In this paper, we give the definition of isoclinism for regular Hom-Lie algebras and verify some of its properties. Finally, we introduce the factor set and show that the isoclinism and isomorphism of two finite same dimensional regular…