Monoidal Morita invariants for finite group algebras |
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Authors: | Kenichi Shimizu |
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Institution: | Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan |
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Abstract: | Two Hopf algebras are called monoidally Morita equivalent if module categories over them are equivalent as linear monoidal categories. We introduce monoidal Morita invariants for finite-dimensional Hopf algebras based on certain braid group representations arising from the Drinfeld double construction. As an application, we show, for any integer n, the number of elements of order n is a monoidal Morita invariant for finite group algebras. We also describe relations between our construction and invariants of closed 3-manifolds due to Reshetikhin and Turaev. |
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