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Malcev Yang-Baxter equation, weighted $mathcal{O}$-operators on Malcev algebras and post-Malcev algebras | | F. Harrathi
; S. Mabrouk
; O. Ncib
; S. Silvestrov
; | | Date: |
8 Jun 2022 | | Abstract: | The purpose of this paper is to study the $mathcal{O}$-operators on Malcev
algebras and discuss the solutions of Malcev Yang-Baxter equation by
$mathcal{O}$-operators. Furthermore we introduce the notion of weighted
$mathcal{O}$-operators on Malcev algebras, which can be characterized by
graphs of the semi-direct product Malcev algebra. Then we introduce a new
algebraic structure called post-Malcev algebras. Therefore, post-Malcev
algebras can be viewed as the underlying algebraic structures of weighted
$mathcal{O}$-operators on Malcev algebras. A post-Malcev algebra also gives
rise to a new Malcev algebra. Post-Malcev algebras are analogues for Malcev
algebras of post-Lie algebras and fit into a bigger framework with a close
relationship with post-alternative algebras. | | Source: | arXiv, 2206.03629 | | Services: | Forum | Review | PDF | Favorites | |
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