The Coefficients Are First-order Cohomology Of The Witt Algebra Over The Tensor Product Of The Modulo Density Tensors

The Witt algebra is an infinite dimensional Lie algebra,It plays an important role in Math-ematics and Physics.At present,Cohomology of Witt algebra has been studies extensively.In this paper,we study the first order cohomology of the Witt algebra with coefficients in tensor product of two tensor density modules.Our main result can be stated as follows:(?)Finally,as an application,we determine?????th0e,L ioe tbhiearlwgiesber.a structures of several classes of infinite dimensional Lie algebras.