Classification of Some Solvable Leibniz Algebras

DEMİR İ., Misra K. C., Stitzinger E.

Algebras and Representation Theory, vol.19, no.2, pp.405-417, 2016 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s10468-015-9580-5
  • Journal Name: Algebras and Representation Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.405-417
  • Keywords: Classification, Leibniz algebra, Nilpotency, Solvability
  • Uşak University Affiliated: Yes

Abstract

Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension ≤ 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.