In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transform at ions over the category of modules of a Yang-space form a group.
In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transposi...In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transpositions.展开更多
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
基金Shanghai Development Fund for SciencesTechnology and by Shanghai Higher-Education Institution Development Fund for Sciences and Technology
文摘The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transform at ions over the category of modules of a Yang-space form a group.
文摘In this paper, author studies the rigidity of quasi-Casimir elements, and associate them with root-systems. Moreover, Yang-Baxter operators are constructed as compositions of quasi-Casimir elements and quasi-transpositions.
