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

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May 2012

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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 Sciences), 2012, (3): 71-84,96.

Citation:

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 Sciences), 2012, (3): 71-84,96.

Citation:

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 Sciences), 2012, (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

1.
Department of Mathematics, East China Normal University, Shanghai 200241, China

Received Date: 2011-09-01
Rev Recd Date: 2011-12-01
Publish Date: 2012-05-25

Abstract

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.
- Casimir element,
- generalized eigenspace,
- indecomposable modules,
- primitive idempotents

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References(1)

References

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