论文标题
Malcev Yang-Baxter方程，加权$ \ Mathcal {O} $ - Malcev代数和Malcev后代数的运营商
Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
论文作者
论文摘要
本文的目的是研究Malcev代数的$ \ Mathcal {O} $ - 运营商，并通过$ \ Mathcal {O} $ - 运算符讨论Malcev Yang-Baxter方程的解决方案。此外，我们介绍了MALCEV代数上加权$ \ Mathcal {O} $ - 运算符的概念，可以通过半独立产品Malcev代数的图表来表征。然后，我们引入了一种新的代数结构，称为Malcev后代数。因此，Malcev后代数可以看作是MALCEV代数上的加权$ \ Mathcal {O} $的基础代数结构。 Malcev后代数也引起了新的Malcev代数。 MALCEV后代数是lie后代数的MALCEV代数的类似物，并适合与后代数有密切关系的更大框架。
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.
