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

华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 71-84,96.

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

仝兆佳, 胡乃红

华东师范大学~~数学系, 上海 200241

收稿日期:2011-09-01 修回日期:2011-12-01 出版日期:2012-05-25 发布日期:2012-05-22

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

TONG Zhao-jia, HU Nai-hong

Department of Mathematics, East China Normal University, Shanghai 200241, China

Received:2011-09-01 Revised:2011-12-01 Online:2012-05-25 Published:2012-05-22

摘要/Abstract

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.

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

中图分类号:

O152

仝兆佳, 胡乃红. $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解[J]. 华东师范大学学报(自然科学版), 2012, 2012(3): 71-84,96.

TONG Zhao-jia, HU Nai-hong. Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(3): 71-84,96.

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