English

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

Rings and Algebras 2024-11-26 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.2409.17184,
  title  = {Anti-Leibniz algebras: A non-commutative version of mock-Lie algebra},
  author = {Safa Braiek and Taoufik Chtioui and Sami Mabrouk},
  journal= {arXiv preprint arXiv:2409.17184},
  year   = {2024}
}

Comments

19 pages (Accepted in Journal of Geometry and Physics)