Rota-Baxter Operators Of Heisenberg Lie Algebra

There is a important value of the theoretic significance of Lie algebra in the course of being found till developing and Lie algebra has always arouse wide concern.In the development of more than a century,the study of the Lie algebra has made good performance no matter which aspects that the structure,the classification or representation of the Lie algebra theory.Nowadays,the scientists try their best to apply the theory of structure and representation to physics and other subjects in order to the Lie algebra theory can apply to the natural science.Since the 21 st century,the study of Rota-Baxter operators theory has vigorous development in mathematics and physics and another natural science.The specific content of this paper is that we calculate the Rota-Baxter operators of Heisenberg Lie algebras,which include the operators of 3-dimensional and5-dimensional Heisenberg Lie algebras.We make a brief introduction about the Heisenberg Lie algebra and the Rota-Baxter operators and realize the history of the development of both of them,as well as the research status at home and abroad.We consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra of(37),where(37)is an algebraic closed field with zero feature,by using the definition of Heisenberg Lie algebra and the characteristics of Lie product and the Lie product of the basis element,all Rota-Baxter operators of3-dimensional Heisenberg Lie algebras are calculated.In addition,the corresponding application is given in this paper.For example,according to the definition of the left symmetric algebra,this paper constructs the left symmetric algebra by use of the Rota-Baxter operators that weight 0 of 3-dimensional Heisenberg Lie algebra(Yang-Baxter).The paper discusses and gets the homomorphic operators of3-dimensional Heisenberg Lie algebra of weight 0 and 1 by using the definition of isomorphism and homomorphism.We find the question of the Rota-Baxter operators of 5-dimensional Heisenberg Lie algebra of(37),an algebraic closed field with zero feature,by using the definition of Heisenberg Lie algebra and the characteristics of Lie product and the Lie productof the basis element,and all Rota-Baxter operators of 5-dimensional Heisenberg Lie algebras are calculated.