Study On One Kind Of Infinite-dimensional Lie Algebras

Lie algebra is widely used in mathematics and physics. Virasoro algebra, themost basic type of Lie algebra, plays a very important role in the study of Lie algebra.This kind of algebraic research work has made many significant achievements, butthere are still many parts to be worth of study. This paper mainly studies the structureof dim L2affine-Virasoro Lie algebra, and focuses on the structure of Liebialgebra of Lie algebra L.There are four parts in my paper, the first part introduces the Lie algebra,Virasoro algebra and Lie bialgebra background and development situation, as well assome necessary basic knowledge. Second part we give the2-cocyclcs and centralextensions over the dim L2affine-Virasoro algebra, and we study the derivationalgebra and the automorphism groups over it too. In the third part of this paper, wemainly studied the Lie bialgebra structures over L, and gave some conclusions of it.Finally we give a conclusion and a forecast to the future.