I-factorial quantum torsors

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.