On modified Rota-Baxter Hom-Lie algebras

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

中文摘要:

      

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 then develop the 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.