Geodesic
Categorical duality for Yetter-Drinfeld algebras
Documenta mathematica, Tome 19 (2014), pp. 1105-1139.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 20G42, 18D10, 46L53, 57T05
Keywords: C^*-tensor category, quantum group, Yetter--Drinfeld algebra, Poisson boundary 
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     title = {Categorical duality for {Yetter-Drinfeld} algebras},
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Neshveyev, Sergey; Yamashita, Makoto. Categorical duality for Yetter-Drinfeld algebras. Documenta mathematica, Tome 19 (2014), pp. 1105-1139. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a7/