Related papers: Description of three-dimensional evolution algebra…
Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.
We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a…
The classification of algebraic structures and their derivations is an important and ongoing research area in mathematics and physics, and various results have been obtained in this field. This article presents the classification of…
In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
The notion of $\delta$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $\delta$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras,…
We are concerned with polynomial involutions in characteristic two. In this note, we look for involutions among triangular automorphisms of the four-dimensional polynomial ring in characteristic two and obtain three types of such…
These notes briefly discuss finite-dimensional algebras with involutions, self-adjoint elements, and so on.
In this paper we classify filiform associative algebras of degree $k$ over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by…
We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…
All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…
The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…
We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of…
The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz--Poisson algebras, transposed Leibniz--Poisson algebras, Novikov--Poisson algebras, commutative pre-Lie algebras, anti-pre-Lie…
Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, $\mathcal {D}^b(A)$ be the bounded derived category of $A$-mod and $A^{(m)}$ be the $m$-replicated algebra of $A$. In this paper, we investigate the structure…
We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra,…
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…
In this paper we introduce the notion of evolution rank and give a decomposition of an evolution algebra into its annihilator plus extending evolution subspaces having evolution rank one. This decomposition can be used to prove that in…
The main objective of this paper is to study the relationship between a solvable evolution algebra and its subalgebra lattice, emphasizing two of its main properties: distributivity and modularity. First, we will focus on the nilpotent…
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.