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

被引：0

作者：

Braiek, Safa ^{[1
]}

Chtioui, Taoufik ^{[2
]}

Mabrouk, Sami ^{[3
]}

机构：

[1] Univ Sfax, Fac Sci, BP 1171, Sfax 3000, Tunisia

[2] Gabes Univ, Fac Sci, Mathemat & Applicat Lab LR17ES11, Gabes, Tunisia

[3] Univ Gafsa, Fac Sci, BP 2100, Gafsa, Tunisia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2025年 / 209卷

关键词：

Mock-Lie algebra; Representation; Leibniz algebra; Anti-Leibniz algebra; Embedding tensor; Averaging operator;

D O I：

10.1016/j.geomphys.2024.105385

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 mockLie 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. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：15

共 25 条

[1] On a type of commutative algebras [J].