Rieffel Deformation of Group Coactions

Abstract

Let G be a locally compact group, γ sub; G an abelian subgroup and let Ψ be a continuous 2-cocycle on the dual group γ. Let B be a C*-algebra and ΔB ε Mor(B,B ⊗ C0(G)) a continuous right coaction. Using Rieffel deformation, we can construct a quantum group (C0(G)Ψ⊗Ψ, ΔΨ) and the deformed C*-algebra BΨ. The aim of this paper is to present a construction of the continuous coaction ΔBΨ of the quantum group (C0(G)Ψ⊗Ψ, ΔΨ) on BΨ. The transition from the coaction ΔB to its deformed counterpart ΔBΨ is nontrivial in the sense that ΔBΨ contains complete information about ΔB. In order to illustrate our construction we apply it to the action of the Lorentz group on the Minkowski space obtaining a C*-algebraic quantum Minkowski space. © 2010 The Author(s).