Rieffel deformation via crossed products

We start from Rieffel data (A, Psi, rho), where A is a C*-algebra, rho is an action of an abelian group Gamma on A and Psi is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C*-algebra A(Psi). In the case of Gamma = R(n) we obtain a very simple proof of invariance of K-groups under the deformation. In the general case we also get a very simple proof that nuclearity is preserved under the deformation. We show how our approach leads to quantum groups and investigate their duality. The general theory is illustrated by an example of the deformation of SL(2, C). A description of it, in terms of noncommutative coordinates (alpha) over cap, (beta) over cap, (gamma) over cap, (delta) over cap, is given. (C) 2009 Elsevier Inc. All rights reserved.