The Structure Of A Class Of Infinite Dimensional Lie Algebras

Virasoro algebra is one of the most basic kind of infinite dimensional Lie algebras,and it is also one of the important subjects in Lie theory.At present,many mathematical researchers have studied the structure and representation of algebra associated with it.In this article,we study a class of infinite dimensional Lie algebras,which contains the Virasoro algebra as a subalgebra and give the 2-cohomology group and derivation subalgebra of such Lie Algebras.With the further study of infinite dimensional Lie algebra,the study of Virasoro algebra has made a new breakthrough in the 80s of last century,and many algebraic structures associated with it have appeared.Virasoro algebra plays a very important role in the study of mathematics and physics and related disciplines.Many researchers in mathematics and physics and related disciplines are interested in the algebraic structure associated with Virasoro algebra,and has carried on the thorough research.The structure theory of Lie algebra mainly includes the study that 2-cohomology group,derivation algebra,automorphism and isomorphism.The researchers combined it with the algebraic model to explore an algebraic system which close to the ring,and it obtained many satisfactory useful results,and then it became a breakthrough in our study of algebra.In 1942,Hoch Hilde specifically and thoroughly studied the algebraic system and combined with algebra,and also calculated the derivative algebra of Lie algebra.Up to now,there are few data and articles about the above Lie Algebras,there are a lot of workers in mathematical and physical to carry out in-depth exploration and research.As the structure of the infinite dimension of Lie algebra with Virasoro Lie algebra as sub-algebra is not perfect,the research of this paper is the improvement and supplement of the present Li theory.On the basis of the structure of Virmaoro algebra as a sub-algebra,a class of infinite dimensional of Lie algebra is discussed further.The first chapter briefly reviews the history of Lie algebra and its related basics.In the second chapter,we give the definition of infinite dimensional of Lie algebra,from which we can see the sub-algebra of Virasoro algebra.Firstly,we construct a linear function for any 2-order cycle of this infinite dimensional of Lie algebra,and the linear function is used to pave the other for the 2-cohomology group inference.Finally,a 2-homology group of infinite dimensional of Lie algebras with Virasoro algebra as sub-algebra is obtained.The third chapter is on the basis of the first two chapters.Firstly,we introduce the concepts of the inner derivative algebra and the outer derivative algebra,and then we calculated and proved the derivative of the infinite dimensional of Lie algebra.