Searcharxiv⌕ Search

arXiv subjects

Safa Braiek

Publications and source records attributed to Safa Braiek.

2 recordsLinked to original sources
arXiv2024

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

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.

math.RA↗
arXiv2023

Hom-associative algebras, Admissibility and Relative averaging operators

We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two characterizations of relative averaging operators of Hom-associative algebras via graphs and Nijenhuis operators. A (homomorphic) relative averaging operator of Hom-associative algebras with respect to a given representation gives rise to Hom-associative (tri)dialgebras. By admissibility, a Hom-Jordan (tri)dialgebra and a Hom-(tri)Leibniz algebra can be obtained from Hom-associative (tri)dialgebra.

math.RA↗