Anti-Leibniz algebras: A non-commutative version of mock-Lie algebra
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912130887843840 |
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| author | Braiek, Safa Chtioui, Taoufik Mabrouk, Sami |
| author_facet | Braiek, Safa Chtioui, Taoufik Mabrouk, Sami |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anti-Leibniz algebras: A non-commutative version of mock-Lie algebra Braiek, Safa Chtioui, Taoufik Mabrouk, Sami Rings and Algebras Representation Theory 16W10, 17A60, 17A01, 17A32, 17A36 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. |
| title | Anti-Leibniz algebras: A non-commutative version of mock-Lie algebra |
| topic | Rings and Algebras Representation Theory 16W10, 17A60, 17A01, 17A32, 17A36 |
| url | https://arxiv.org/abs/2409.17184 |