$overline{emph{textbf{U}}}_{{bm r},{bm s}}textbf{(}{bm sl}_{bf 2}textbf{)}$,关于主不可分解模的直和分解

描述了限制型双参数量子群,$overline{U}_{r,s}(sl_2)$,的一类不可约模, 构造出,$overline{U}_{r,s}(sl_2)$,所有的主不可分解模. 把,Casimir,元素的左乘作用看作,$overline{U}_{r,s}(sl_2)$,到自身的线性变换, 得到了,Casmir,元素作用在,$overline{U}_{r,s}(sl_2)$,上的极小多项式和,$overline{U}_{r,s}(sl_2)$,本原幂等元的全部共轭类.

Direct sum decomposition of $overline{emph{textbf{U}}}_{{bm r},{bm s}}textbf{(}{bm s}{bm l}_{bf 2}textbf{)}$ about principal indecomposable modules

This paper described a class of irreducible modules of the restricted two-parameter quantum group $overline{U}_{r,s}(sl_2)$, and constructed all its principal indecomposable modules.  Finally, the minimal polynomial of the action of the Casimir element on $overline{U}_{r,s}(sl_2)$ and all the conjugate classes of the
primitive idempotents of $overline{U}_{r,s}(sl_2)$ were obtained.