Diassociative algebras and their derivations

Abstract. Considering significant of classification problems in modern algebra, especially in the algebras which related to Lie algebras, current research pursue investigation on structure theory of low dimensional diassociative algebras. Note that the classification of complex diassociative algebras in low dimensions have been presented in our recent studies, however this paper deals to provide description of such algebras with some constrains in dimension three, applying notion of annihilator.

Section: Resultsmentioning

confidence: 99%

“…We would like to note that in our recent papers we considered classification of diassociative algebras in dimension two and three [5], [9]. Where, we obtained list of diassociative algebras using Associative algebras in respective dimensions.…”

Section: Zinb As Leib Com Liementioning

confidence: 99%

Alternative description of three dimensional complex diassociative algebras with some constraints

Rikhsiboev

Venkatesan

2014

Algorithms for computations of Loday algebras’ invariants

Hussain¹,

Rakhimov²,

Basri³

2017

The paper is devoted to applications of some computer programs to study structural determination of Loday algebras. We present how these computer programs can be applied in computations of various invariants of Loday algebras and provide several computer programs in Maple to verify Loday algebras' identities, the isomorphisms between the algebras, as a special case, to describe the automorphism groups, centroids and derivations.

Centroids and derivations of low-dimensional Leibniz algebra

Husain

Rakhimov

Basri

2017

In this paper we introduce the concept of centroid and derivation of Leibniz algebras. By using the classification results of Leibniz algebras obtained earlier, we describe the centroids and derivations of low-dimensional Leibniz algebras. We also study some properties of centroids of Leibniz algebras and use these properties to categorize the algebras to have socalled small centroids. The description of the derivations enables us to specify an important subclass of Leibniz algebras called characteristically nilpotent.