量子环面上导子李代数的一类不可约权模

A Class of Weight Modules for the Derivation Lie Algebras of Quantum Tori

量子环面是一类重要的非交换环面,它与高维仿射李代数的关系十分密切,它的导子李代数也在高维仿射李代数的表示理论里有着重要的作用.设D是一个有n+1个变量的量子环面,且其中有n个变量是相互交换的.本文对量子环面D的导子李代数给出了一类权模,证明这些模是权空间有限维的不可约模,并决定了它们的权的支集.

Quantum torus Is a very important class of non-commutative torus.Not only it has a close relation with the extended affine Lie algebra, but also its derivation Lie algebra plays a significant role in the representation theory of the extended affine Lie algebra. Let D be a quantum torus with n＋1 variables with n of them commuting. In this paper, we study a class of weight modules for the derivation Lie algebra of the quantum torus D. We show that these modules are irreducible and occupy finite dimensional weight spaces. Furthermore, their supports are calculated explicitly.