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Categorical dualtiy for Yetter-Drinfeld C*-algebras. Beyond the braided-commutative case (2504.21162v1)
Published 29 Apr 2025 in math.OA and math.QA
Abstract: We develop a tensor categorical duality in the sprit of the Tannaka-Krein duality for the C*-algebras admitting the Yetter-Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G, the Yetter-Drinfeld G-C*-algebras correspond to the bimodule categories over the representation category Rep(G), satisfying a certain centrality condition.