Frobenius-Schur indicator for categories with duality

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1 Citation (Scopus)


We introduce the Frobenius-Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius-Schur theorem including that for semisimple quasi-Hopf algebras, weak Hopf C*-algebras and association schemes. Our framework also clarifies a mechanism of how the "twisted" theory arises from the ordinary case. As a demonstration, we establish twisted versions of the Frobenius-Schur theorem for various algebraic objects. We also give several applications to the quantum SL2.

Original languageEnglish
Pages (from-to)324-364
Number of pages41
Issue number3
Publication statusPublished - 2012 Dec 1
Externally publishedYes


  • Category with duality
  • Frobenius-Schur indicator
  • Hopf algebra
  • Quantum groups

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology


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