A Class Of Virasoro Lie Algebras

In this paper, we study the derivation and center extension of two kinds of in?nite-dimensional Lie algebras of Virasoro-type which is realized as an a?nization of a 3-dimensional Novikov algebra.First of all, we introduce the development and studying trend of the Lie algebras, Novikov algebras and Virasoro algebras. The purpose and signi?cance are also introduced in this paper.Secondly, we study the derivation of an in?nite-dimensional Lie algebra of Virasoro-type which is realized as an a?nization of a 3 dimensional Novikov algebra. Through the conversion of special element, it is proved that the Lie algebra has only one outer derivation in the process of isomorphism.Finally, we calculate the central extension of an in?nite-dimensional Lie algebra of Virasoro-type which is realized as an a?nization of a 3-dimensional Novikov algebra. By calculating the generators, we get the second cohomology group and dimension of the virasoro-type Lie algebra, and then get the universal center extension of the Lie algebra.