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Algebra and Discrete Mathematics, 2020, Volume 29, Issue 1, Pages 52–65
DOI: https://doi.org/10.12958/adm1165 (Mi adm738) 		 
RESEARCH ARTICLE

Leibniz algebras with absolute maximal Lie subalgebras

G. R. Biyogmama, C. Tchekab

a Department of Mathematics, Georgia College & State University, Campus Box 17 Milledgeville, GA 31061-0490
b Department of Mathematics, University of Dschang, Dschang, Cameroun
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DOI: https://doi.org/10.12958/adm1165
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.
Received: 15.05.2018
Bibliographic databases:
Document Type: Article
MSC: 17A32, 17B55, 18B99
Language: English
Citation: G. R. Biyogmam, C. Tcheka, “Leibniz algebras with absolute maximal Lie subalgebras”, Algebra Discrete Math., 29:1 (2020), 52–65
Citation in format AMSBIB
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\by G.~R.~Biyogmam, C.~Tcheka
\paper Leibniz algebras with absolute maximal Lie subalgebras
\jour Algebra Discrete Math.
\yr 2020
\vol 29
\issue 1
\pages 52--65
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\crossref{https://doi.org/10.12958/adm1165}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085119507}
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