Monoidal Morita invariants for finite group algebras

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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.

Original languageEnglish
Pages (from-to)397-418
Number of pages22
JournalJournal of Algebra
Volume323
Issue number2
DOIs
Publication statusPublished - 2010 Jan 15
Externally publishedYes

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Keywords

  • Hopf algebras
  • Monoidal categories
  • Monoidal Morita theory

ASJC Scopus subject areas

  • Algebra and Number Theory

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