Categorical aspects of cointegrals on quasi-Hopf algebras

Taiki Shibata, Kenichi Shimizu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Hopf algebra H, we give an explicit description of categorical cointegrals of the category MH of left H-modules in terms of cointegrals on H. Provided that H is unimodular, we also express the Frobenius structure of the ‘adjoint algebra’ in the Yetter-Drinfeld category YHHD by using an integral in H and a cointegral on H. Finally, we give a description of the twisted module trace for projective H-modules in terms of cointegrals on H.

Original languageEnglish
Pages (from-to)353-411
Number of pages59
JournalJournal of Algebra
Publication statusPublished - 2020 Dec 15


  • Cointegral
  • Integral
  • Module trace
  • Quasi-Hopf algebra
  • Tensor category
  • Yetter-Drinfeld category

ASJC Scopus subject areas

  • Algebra and Number Theory


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