Related papers: The classification of $2$-dimensional rigid algebr…

In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…

The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.

Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple…

Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal 2-category. Examples of rigid algebras include…

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…

In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.

The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an…

This paper is devoted to the complete algebraic and geometric classification of complex 4 and 5-dimensional antiassociative algebras. In particular, we proved that the variety of complex 4-dimensional antiassociative algebras has dimension…

This paper introduces a categorification of $k$-algebras called 2 -algebras, where k is a commutative ring. We define the 2-algebras as a 2-category with single object in which collections of all 1-morphisms and all 2-morphisms are…

In the present paper we prove that every local and $2$-local derivation on conservative algebras of $2$-dimensional algebras are derivations. Also, we prove that every local and $2$-local automorphism on conservative algebras of…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids…

In this paper we give classification of two-dimensional real evolution algebras. For several chains of evolution algebras we study their classification dynamics.

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…

We give algebraic and geometric classifications of $4$-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are $41$ one-parameter families of $4$-dimensional nilpotent terminal (non-Leibniz)…

A complete classification of a class of $3$-dimensional algebras is provided. In algebraically closed field $\mathbb{F}$ case this class is an open, dense (in Zariski topology) subset of $\mathbb{F}^{27}$.

We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable.…