Generalized fixed-point algebras for twisted C⁎-dynamical systems

Abstract

We show that Ralf Meyer's method of constructing generalized fixed-point algebras for C⁎-dynamical systems via their square-integrable representations on Hilbert C⁎-modules works for twisted C⁎-dynamical systems. To do this, we introduce the category of twisted Hilbert C⁎-modules and prove that Meyer's bra-ket operators are morphisms in this category. Some non-trivial results that we can obtain are a twisted-equivariant version of Kasparov's Stabilization Theorem and the existence of a classifying category for the category of Hilbert modules over any fixed reduced twisted crossed product. Furthermore, an interesting connection is made to the Gabor-analytic method of constructing Hilbert modules over non-commutative tori by Franz Luef.