Monoidal Morita invariants for finite group algebras

Details Monoidal Morita invariants for finite group algebras Monoidal Morita invariants for finite group algebras

2009-05-08

arxiv.org/abs/0905.1185v2

Mathematics

Quantum Algebra

25 pages; To appear in J. of Algebra. Main modifications are the following: (i) Verbose parts of the paper were summarized. (i

Scientific paper

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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