EQUIVARIANT DEFORMATIONS OF HOMOGENEOUS SPACES

C-algebraic deformations of homogeneous spaces G/Gamma are constructe d by completing dense subspaces of C-0(G/Gamma) in a different multipl ication and C-norm; these deformations are equivariant in the sense t hat they still carry a natural action of G by left translation. The mo tivating examples are the noncommutative Heisenberg manifolds of Rieff el, but the construction given here is based on the authors' twisted d ual-group algebras, which are equivariant deformations of C-0(G). The procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simple C- algebras. (C) 1997 Academic Press.