Geodesic
Categorical duality for Yetter-Drinfeld algebras
Documenta mathematica, Tome 19 (2014), pp. 1105-1139
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We study tensor structures on (RepG)-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 RepG into C∗-tensor categories. To illustrate this equivalence, we discuss coideals of quotient type in C(G), Hopf–Galois extensions and noncommutative Poisson boundaries.
DOI : 10.4171/dm/476
Classification : 20G42, 46L53, 57T05
Mots-clés : quantum group, Poisson boundary, C\^\*-tensor category, Yetter--Drinfeld algebra 
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     title = {Categorical duality for {Yetter-Drinfeld} algebras},
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     doi = {10.4171/dm/476},
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Sergey Neshveyev; Makoto Yamashita. Categorical duality for Yetter-Drinfeld algebras. Documenta mathematica, Tome 19 (2014), pp. 1105-1139. doi: 10.4171/dm/476

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