Semisimplicity of Certain Representation Categories

Semisimplicity of Certain Representation Categories

We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl decomposition of the corresponding sub-bimodule. Finally, we u...

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Main Author: Foster, John
Other Authors: Berenstein, Arkady
Language:en_US
Published: University of Oregon 2013
Subjects:
Online Access:http://hdl.handle.net/1794/13269
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spelling ndltd-uoregon.edu-oai-scholarsbank.uoregon.edu-1794-132692018-12-20T05:48:09Z Semisimplicity of Certain Representation Categories Foster, John Berenstein, Arkady We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl decomposition of the corresponding sub-bimodule. Finally, we use this technique to establish the semisimplicity of certain finite-dimensional representations of the quantum double $D(U_q(sl_2))$ for generic $q$. 2013-10-03T23:33:29Z 2013-10-03T23:33:29Z 2013-10-03 Electronic Thesis or Dissertation http://hdl.handle.net/1794/13269 en_US All Rights Reserved. University of Oregon
collection NDLTD
language en_US
sources NDLTD
topic
spellingShingle
Foster, John
Semisimplicity of Certain Representation Categories
description We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl decomposition of the corresponding sub-bimodule. Finally, we use this technique to establish the semisimplicity of certain finite-dimensional representations of the quantum double $D(U_q(sl_2))$ for generic $q$.
author2 Berenstein, Arkady
author_facet Berenstein, Arkady
Foster, John
author Foster, John
author_sort Foster, John
title Semisimplicity of Certain Representation Categories
title_short Semisimplicity of Certain Representation Categories
title_full Semisimplicity of Certain Representation Categories
title_fullStr Semisimplicity of Certain Representation Categories
title_full_unstemmed Semisimplicity of Certain Representation Categories
title_sort semisimplicity of certain representation categories
publisher University of Oregon
publishDate 2013
url http://hdl.handle.net/1794/13269
work_keys_str_mv AT fosterjohn semisimplicityofcertainrepresentationcategories
_version_ 1718804168766914560

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