Rieffel deformation and twisted crossed products

Abstract

To a continuous action of a vector group on a $C^*$-algebra, twisted by the imaginary exponential of a symplectic form, one associates a Rieffel deformed algebra as well as a twisted crossed product. We show that the second one is isomorphic to the tensor product of the first one with the $C^*$-algebra of compact operators in a separable Hilbert space and we indicate some applications.