Anti-Leibniz algebras: A non-commutative version of mock-Lie algebra

2024/09/24 by Braiek, Safa, Chtioui, Taoufik, Mabrouk, Sami · 1 citation
#16W10 #17A01 #17A32 #17A36 #17A60 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2409.17184

Abstract

Leibniz algebras are non skew-symmetric generalization of Lie algebras. In this paper we introduce the notion of anti-Leibniz algebras as a "non commutative version" of mock-Lie algebras. Low dimensional classification of such algebras is given. Then we investigate the notion of averaging operators and more general embedding tensors to build some new algebraic structures, namely anti-associative dialgebras, anti-associative trialgebras and anti-Leibniz trialgebras.

Cited by

• Extensions of pseudo-euclidean mock-Lie superalgebras

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