厦门大学学报（自然科学版）2009，Vol.48Issue(4)：464-466,3.
Loop代数的有限维不可约模的导子
The Derivations of the Finite Dimensional Irreducible Modules over the Loop Algebras
摘要
Abstract
Let G be a simple Lie algebra over the complex field C,A=C[t±1], and GA: =GCA be the loop algebra. For any nonzero complex number a and any finite dimensional irreducible G-module M, Ma: =M is an irreducible GA-module. Where, the the action of x f(t) on Ma is defined by sending m to f(a)xm. In this paper, the author firstly proved that if any finite dimensional modules of Lie algebra L is completely reducible, then the derivations of such modules are all inner derivations. Using the fact that any finite dimensional modules of a complex simple Lie algebra is completely reducible, he computed the derivations of GA-module Ma,and proved that there exists outer derivations of Ma if and only if M is G's adjoint module.关键词
loop代数/不可约模/导子Key words
loop algebra/ irreducible module/ derivation分类
数理科学引用本文复制引用
连海峰..Loop代数的有限维不可约模的导子[J].厦门大学学报（自然科学版）,2009,48(4):464-466,3.基金项目
国家自然科学基金(10671160) 资助 （10671160）
