关于修正罗巴Hom-李代数

On Modified Rota-Baxter Hom-Lie Algebras

中文关键词:  Hom-李代数  修正罗巴算子  上同调  形变  阿贝尔扩张

英文关键词:Hom-Lie algebra  modified Rota-Baxter operator  cohomology  deformation  abelian extension

中文摘要:

      Semenov-Tian-Shansky给出了修正经典杨-巴克斯特方程的解,称为修正$r$-矩阵.最近相关的研究成为热点课题.本文引入修正罗巴Hom-李代数的概念和表示.然后发展修正罗巴Hom-李代数的上同调,系数取自表示.作为应用,利用二阶上同调群研究修正罗巴Hom-李代数的形式形变和阿贝尔扩张.

英文摘要:

      Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified $r$-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified Rota-Baxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.