$\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解
Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules
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摘要: 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.
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关键词:
- Casimir\,元素 /
- 广义特征子空间 /
- 主不可分解模 /
- 本原幂等元
Abstract: 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.-
Key words:
- Casimir element /
- generalized eigenspace /
- indecomposable modules /
- primitive idempotents
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