Expansion Algebraic Structure. Witt Algebra And

In this paper, we mainly study the structure and the representation theoryof the extended Witt algebra L. In Chapter 1, we introduce the background, thesigni?cance and the development of the Witt algebra and the extended Witt algebraL. In Chapter 2, we firstly introduce the de?nition of the derivation and somepreliminary knowledge about it. Then we get some lemmas and a theorem. InChapter 3, we firstly review the conception of 2-cocycle and study the 2-cocycle of Liealgebra L. Then we de?ne the central extension and the universal central extension.Secondly, we review the Leibniz algebra, and study the universal central extensionof L in the category of Leibniz algebra. Lastly, we study the representation theoryof the universal central extension, and we focus on the classi?cation of irreducibleweight modules about it.