Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dime...Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.展开更多
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...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 RotaBaxter 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.展开更多
基金National Natural Science Foundation of China(11971315)。
文摘Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘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 RotaBaxter 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.
