I-factorial quantum torsors

TL;DR

This paper studies a special class of quantum torsors called I-factorial quantum torsors, exploring their duality properties and providing examples such as the Heisenberg double, extending the theory of quantum group deformations.

Contribution

It introduces the study of I-factorial quantum torsors and develops their duality theory, expanding the framework of quantum group deformations and torsor constructions.

Findings

I-factorial quantum torsors have a well-defined duality theory.

The Heisenberg double serves as a key example illustrating the theory.

Quantum torsors can be constructed from dual quantum group actions on type I-factors.

Abstract

In an earlier paper of the author, locally compact quantum torsors were defined for locally compact quantum groups, putting into the analytic framework the theory of Galois objects for Hopf algebras. Such quantum torsors allow to deform the given quantum group, providing a generalization of the 2-cocycle twisting procedure. It was also shown that a quantum torsor can be constructed from an action of the dual quantum group on a type I-factor. In this paper, we study quantum torsors which are themselves type I-factors. These I-factorial quantum torsors turn out to have a nice duality theory. We illustrate the general theory with the example of the Heisenberg double.