RESEARCH ARTICLE

Leibniz algebras with absolute maximal Lie subalgebras

G. R. Biyogmam^a, C. Tcheka<sup>b

a</sup> Department of Mathematics, Georgia College & State University, Campus Box 17 Milledgeville, GA 31061-0490
^b Department of Mathematics, University of Dschang, Dschang, Cameroun

Abstract: A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their $\mathsf{Lie}$-center are greater than two, we refer to these Leibniz algebras as $s$-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz $s$-algebras of dimension up to five.

Keywords: Leibniz algebras, $s$-Leibniz algebras, $\mathsf{Lie}$-center.

MSC: 17A32, 17B55, 18B99

Received: 15.05.2018

Language: English

DOI: 10.12958/adm1165

Bibliographic databases:

• 
•