Monoidal Morita invariants for finite group algebras

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Keywords

  • Hopf algebras
  • Monoidal categories
  • Monoidal Morita theory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Monoidal Morita invariants for finite group algebras. / Shimizu, Kenichi.

In: Journal of Algebra, Vol. 323, No. 2, 15.01.2010, p. 397-418.

Research output: Contribution to journalArticle

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