Quantum group-twisted tensor products of C*-algebras

TL;DR

This paper introduces a novel noncommutative tensor product of C*-algebras using quantum group coactions and bicharacters, providing two equivalent constructions and exploring their properties and examples.

Contribution

It presents a new framework for quantum group-twisted tensor products of C*-algebras with dual constructions and foundational properties.

Findings

Two equivalent constructions of the twisted tensor product.

Basic properties established for the new tensor product.

Examples illustrating the application of the theory.

Abstract

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. The first construction is based on certain pairs of representations of quantum groups which we call Heisenberg pairs because they generalise the Weyl form of the canonical commutation relations. The second construction uses covariant Hilbert space representations. We establish basic properties of the twisted tensor product and study some examples.