Related papers: Counting finite-dimensional algebras over finite f…
We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension less than 7 over a finite field.
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the variety of Leibniz algebras. It is shown that, up to isomorphism, there exist three…
In this paper, we present a general method for constructing finite-dimensional quasi-Hopf algebras from finite abelian groups and braided vector spaces of Cartan type. The study of such quasi-Hopf algebras leads to the classification of…
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…
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 give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
Extending the results of [Asian J. Math. 2019], in [Doc. Math. \textbf{21}, 2016] we calculated explicitly the number of isomorphism classes of superspecial abelian surfaces over an arbitrary finite field of \textit{odd} degree over the…
We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them…
Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
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.
We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
A new dimension function on countable-dimensional algebras (over a field) is described. Its dimension values for finitely generated algebras exactly fill the unit interval $[0,1]$. Since the free algebra on two generators turns out to have…
We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions over a dihedral group D_m, with m=4a> 11. We obtain this…
We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.