Leibniz Algebras: Structure and Classification is designed to introduce the reader to the
theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These …

Leibniz algebras are certain generalization of Lie algebras. In this paper we collect and
prove some of the important results in Leibniz algebras which are analogs of corresponding …

Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the
classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical …

One of the key tendencies in the development of Leibniz algebra theory is the search for
analogues of the basic results of Lie algebra theory. In this survey, we consider the reverse …

Abstract Let\(L\) be an algebra over a field\(F\) with the binary operations\(+\)
and\([\,\cdot\,{,}\,\cdot\,]\). Then\(L\) is called a left Leibniz algebra if\([[a, b], c]=[a,[b, c]]-[b,[a …

This paper is devoted to the study of structure of Leibniz algebras. The classical methods to
obtain classifications are essentially to solve a system of equations given by the identities of …

Leibniz algebras are certain generalization of Lie algebras. In this paper we give the
classification of $5-$ dimensional complex non-Lie nilpotent Leibniz algebras. We use the …

Let L be an algebra over a field F with binary operations+ and [·,·]. Then we call L a (left)
Leibniz algebra if it satisfies the (left) Leibniz identity [[a, b], c]=[a,[b, c]]−[b,[a, c]] for all a, b, c …

In this paper, contractions of complex Leibniz algebras are considered. A short summary of
the history, relationships of different definitions and comparisons of them are given. We …

This article is a contribution to the improvement of classification theory in Leibniz algebras.
We extend the method of congruence classes of matrices of bilinear forms that was used to …