Symmetric Self - Dual Structures Of Loop Algebra

The symmetric self dual structure of finite dimensional Lie algebras can be extended to Loop algebras, and a new concept of symmetric self dual structure of Loop algebras is obtained. On this basis, we further study the symmetric self dual structure of Loop algebras. We explore the Loop algebra of symmetric self dual structure of the relevant conclusion.This paper is divided into three chapters:The first chapter: the basic concepts of the bilinear form of the lie algebra are reviewed and the symmetric self dual structure of the Loop algebra is constructed.The second chapter: A special class of symmetric self dual Lie algebra properties.The third chapter: General properties of the symmetric self dual structure of Loop algebras.