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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| Language: | en_US |
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University of Oregon
2013
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| Online Access: | http://hdl.handle.net/1794/13269 |
| Summary: | 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 $q$. |
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