量子代数有限型模权空间的若干性质

Some properties of weight space of finite type module of quantum algebras

令M是Z[v]的由v-1和奇素数p生成的理想,U是A=Z[v]M上相伴于对称Cartan矩阵的量子代数。若U模M作为A模是有限生成的,则称M为有限型U模。给出了量子代数有限型模权空间的若干性质。

Let M be the ideal in Z？v？ generated by v？1 and an odd prime p, U be a quantum algebra over A？Z？v？M with a symmetric Cartan matrix. M was said to be finite type U -module if U -module M as A-module was finitely generated. In this paper, we give some properties of weight space of finite type module of quantum algebras.