Sutanu Roy

QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

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

We construct a maximal counterpart to the minimal quantum group-twisted tensor product of

Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach

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Quantum Symmetries of the Twisted Tensor Products of C*-Algebras

-algebras studied by Meyer, Roy and Woronowicz, which is universal with respect to representations satisfying braided commutation relations. Much like the minimal one, this product yields a monoidal structure on the coactions of a quasi-triangular

Duality for Convex Monoids

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Quantum group-twisted tensor products of C*-algebras. II

-quantum group, the horizontal composition in a bicategory of Yetter-Drinfeld

Homomorphisms of quantum groups

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C*-quantum groups with projection

-algebras, and coincides with a Rieffel deformation of the non-twisted tensor product in the case of group coactions.

The Drinfeld double for

C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford’s Theorem about Hopf algebras with projection suggests that any C*-quantum group with projection decomposes uniquely into an ordinary C*-quantum group and a “braided” C*-quantum group. We establish this on the level of manageable multiplicative unitaries.

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We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns out to be the generalized Drinfeld double of the quantum symmetry groups of the original filtrations. We show how these results apply to a wide class of crossed products of C*-algebras by actions of discrete groups. We also discuss an example where the hypothesis of our main theorem is not satisfied and the quantum symmetry group is not a generalized Drinfeld double.