On extensions of Leibniz algebras

This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it t...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-09, Vol.890 (1), p.12119
Main Authors: Rakhimov, I. S., Said Husain, Sh. K., Mohammed, M. A.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Classification
Fields (mathematics)
Physics
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Summary:This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it to classify four-dimensional Leibniz algebras over a field K. We obtain complete classification of four-dimensional nilpotent Leibniz algebras. The main idea of the method is to transfer the "base change" action to an action of automorphism group of the algebras of smaller dimension on cocycles constructed by the annihilator extensions. The method can be used to classify low-dimensional Leibniz algebras over other finite fields as well.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/890/1/012119