Berenstein, ArkadyFoster, John2013-10-032013-10-032013-10-03https://hdl.handle.net/1794/13269We 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 $q$.en-USAll Rights Reserved.Electronic Thesis or Dissertation