The maximal quantum group-twisted tensor product of C*-algebras

Abstract

We construct a maximal counterpart to the minimal quantum group-twisted tensor product of C*-algebras studied by Meyer, Roy and Woronowicz [16, 17], which is universal with respect to representations satisfying certain braided commutation relations. Much like the minimal one, this product yields a monoidal structure on the coactions of a quasi-triangular C*-quantum group, the horizontal composition in a bicategory of Yetter–Drinfeld C*-algebras, and coincides with a Rieffel deformation of the non-twisted tensor product in the case of group coactions.