Classification of some Solvable Leibniz Algebras

Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension \(\leq 8\) with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Demir, Ismail, Misra, Kailash C, Stitzinger, Ernie
Format: Article
Language:English
Subjects:
Algebra
Canonical forms
Classification
Lie groups
Online Access:Get full text
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Summary:Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension \(\leq 8\) with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain our result. Our approach can easily be extended to classify these algebras of higher dimensions. We also revisit the classification of three dimensional non-Lie solvable (left) Leibniz algebras.
ISSN:2331-8422
DOI:10.48550/arxiv.1501.00890