Malcev Yang-Baxter equation, weighted $\\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras

Authors : Fattoum Harrathi, Sami Mabrouk, Othmen Ncib, Sergei Silvestrov

Pages : 1151-1171

Doi:10.15672/hujms.1126978

View : 181 | Download : 203

Publication Date : 2023-10-31

Article Type : Research Paper

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.
Keywords : Alternative algebra, Malcev algebra, weighted \\mathcal O operators, Rota Baxter operator, representation, Malcev Yang Baxter equation