Semisimplicity of certain representation categories

2015/09/04 by Foster, John E.
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1509.01633

Abstract

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 of sl₂ for generic q.

Related

• Module categories over representations of SL_q(2) in the non-semisimple case
• Module categories over representations of SL_q(2) and graphs
• On semisimplification of tensor categories
• Duality in the Category of Andersen-Jantzen-Soergel
• The representation category of the quantum group of a non-degenerate bilinear form