Monoidal Morita invariants for finite group algebras
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 , the number of elements of order 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.
Keywords
Cite
@article{arxiv.0905.1185,
title = {Monoidal Morita invariants for finite group algebras},
author = {Kenichi Shimizu},
journal= {arXiv preprint arXiv:0905.1185},
year = {2009}
}
Comments
25 pages; To appear in J. of Algebra. Main modifications are the following: (i) Verbose parts of the paper were summarized. (ii) Theorem 6.3 is added. (iii) The relation between Theorem 1.1 and works of Ng and Schauenburg is added