Categorical duality for Yetter-Drinfeld algebras

  • Sergey Neshveyev

    Department of Mathematics Department of Mathematics University of Oslo Ochanomizu University P.O. Box 1053 Blindern Otsuka 2-1-1 NO-0316 Oslo, Norway 192-0361 Tokyo, Japan
  • Makoto Yamashita

    Department of Mathematics Department of Mathematics University of Oslo Ochanomizu University P.O. Box 1053 Blindern Otsuka 2-1-1 NO-0316 Oslo, Norway 192-0361 Tokyo, Japan
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Abstract

We study tensor structures on -module categories defined by actions of a compact quantum group on unital C-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of to the structure of a braided-commutative Yetter–Drinfeld algebra. This shows that the category of braided-commutative Yetter–Drinfeld -C-algebras is equivalent to the category of generating unitary tensor functors from into C-tensor categories. To illustrate this equivalence, we discuss coideals of quotient type in , Hopf–Galois extensions and noncommutative Poisson boundaries.

Cite this article

Sergey Neshveyev, Makoto Yamashita, Categorical duality for Yetter-Drinfeld algebras. Doc. Math. 19 (2014), pp. 1105–1139

DOI 10.4171/DM/476