Abstract
Let G1⊂G be a closed subgroup of a locally compact group G and let X=G/G1 be the quotient space of left cosets. Let X=(C0(X),ΔX) be the corresponding G-C*-algebra where G=(C0(G),Δ). Suppose that Γ is a closed abelian subgroup of G1 and let ψ be a 2-cocycle on the dual group Γ̂. Let Gψ be the Rieffel deformation of G. Using the results of the previous paper of the author we may construct Gψ-C*-algebra Xψ - the Rieffel deformation of X. On the other hand we may perform the Rieffel deformation of the subgroup G1 obtaining the closed quantum subgroup G1ψ⊂Gψ, which in turn, by the results of S. Vaes, leads to the Gψ-C*-algebra Gψ/G1ψ. In this paper we show that Gψ/G1ψ≅Xψ. We also consider the case where Γ⊂G is not a subgroup of G1L, for which we cannot construct the subgroup G1ψ. Then generically Xψ cannot be identified with a quantum quotient. What may be shown is that it is a Gψ-simple object in the category of Gψ-C*-algebras.
| Original language | English |
|---|---|
| Journal | Journal of Functional Analysis |
| Volume | 260 |
| Issue number | 1 |
| Pages (from-to) | 146-153 |
| ISSN | 0022-1236 |
| DOIs | |
| Publication status | Published - 1 Jan 2011 |