Journal of East China Normal University(Natural Sc ›› 2012, Vol. 2012 ›› Issue (3): 71-84,96.

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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   

  1. 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

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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