Equivariant Deformations of Homogeneous Spaces

Abstract

C*-algebraic deformations of homogeneous spacesG/Γare constructed by completing dense subspaces ofC0(G/Γ) in a different multiplication andC*-norm; these deformations are equivariant in the sense that they still carry a natural action ofGby left translation. The motivating examples are the noncommutative Heisenberg manifolds of Rieffel, but the construction given here is based on the authors' twisted dual-group algebras, which are equivariant deformations ofC0(G). The procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simpleC*-algebras