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arXiv · 1310.4407

Categorical duality for Yetter-Drinfeld algebras

Sergey Neshveyev·Makoto Yamashita
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Abstract

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

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BibTeXRIS

Sergey Neshveyev, Makoto Yamashita. 2013-10-16. Categorical duality for Yetter-Drinfeld algebras. https://doi.org/10.4171/dm%2F476

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