Related papers: Complete lists of low dimensional complex associat…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
The present paper is devoted to the complete classification of $4$-dimensional complex Poisson algebras, taking into account a classification, up to isomorphism, of the complex commutative associative algebras of dimension $4$, as well as…
This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of…
We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We…
A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investigate and classify compatible pairs of associative algebras 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.
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…
We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension less than 7 over a finite field.
This study focuses on the analysis of derivations, centroids, and inner derivations of 5-dimensional complex nilpotent associative algebras. It presents the classification of these algebras of dimension less than five, as well as the…
We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
The paper aims to investigate the classification problem of low dimensional complex none Lie filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded none…
In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as…
In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL_4(F). In particular we provide explicit representatives for such classes…
This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller…
In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform associative algebras.
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…