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

TL;DR

This paper introduces a maximal quantum group-twisted tensor product of C*-algebras, providing a universal construction that extends the minimal version and preserves key algebraic structures.

Contribution

It constructs a maximal quantum group-twisted tensor product of C*-algebras, complementing the existing minimal version and establishing its universal properties.

Findings

Defines a maximal twisted tensor product with universal property.

Establishes the product as a monoidal structure on coactions.

Shows the product coincides with Rieffel deformation in specific cases.

Abstract

We construct a maximal counterpart to the minimal quantum group-twisted tensor product of $C^{*}$-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 $C^{*}$-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.