多重Loop李代数的Weyl模

Abstract

设g为任意有限维复单李代数及Aν=C[T1±1,…,Tν±]为ν个交换变量的lAurEnT多项式环.令l(g)=g C[T1±1,…,Tν±]为多重lOOP李代数.考虑l(g)上的WEyl模,证明了这类模都是有限维的,并且在适当的条件下证明了由一个元素生成的多重lOOP代数的模一定是WEyl模的同态像.最后给出了WEyl模的一个张量积分解.

Let g be any finite-dimensional simple Lie algebra over the complex field C and Aν=C[t±11,…,t±1ν] be the Laurent polynomial ring in ν commutating variables.Let L(g)=g C[t±11,…,t±1ν] be an iterated loop algebra.We consider the Weyl modules over L(g).We prove that the Weyl modules are finite-dimensional and any module under some assumption is a quotient of such a module.Finally,we give a tensor product decomposition for the Weyl modules.