Bz Derivations For The Lie Algebra Of Anti-Symmetric Matrices Over A Commutative Ring

The study of Lie algebras has two major directions:the structure and representation of the Lie algebra. Derivation is an important tool for studying the structure of the Lie algebra. In recent years, many scholars promote the concept of derivation to get Lie triple derivation, BZ derivation and so on.In this paper, we mainly study that the decomposition of any BZ derivation of the anti-symmetric matrix Lie algebra Ln(R). The specific content is organized as follows:In Chapter1, we introduce the evolution, development of Lie algebras and the background of the paperIn Chapter2, some essential definitions and preliminary theorems of Lie algebras are in-troduced.In Chapter3, by studying the coefficients of the expression about the BZ derivation, we get an equal relationship between certain coefficients in the different expressions. And then we prove that the decomposition form for any BZ derivation of Ln(R) and the form of this decomposition is unique.In Chapter4, according to the conclusion of the third chapter, we discuss the derivation for the Lie algebra of anti-symmetric matrices.