Rieffel deformation of homogeneous spaces

Rieffel Deformation via Crossed Products

We present a refinement of Rieffel Deformation of C∗-algebras. We start from Rieffel data (A,Ψ, ρ), where A is a C∗-algebra, ρ is an action of abelian group Γ on A and Ψ is a 2-cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C∗-algebra A. In case of Γ = R we obtain a very simple proof of invariance of K-groups under the deformation. In any case we get a sim...

Rieffel Type Discrete Deformation of Finite Quantum Groups

We introduce a discrete deformation of Rieffel type for finite (quantum) groups. Using this, we give an example of a finite quantum group A of order 18 such that neither A nor its dual can be expressed as a crossed product of the form C(G1) ⋊τ G2 with G1 and G2 ordinary finite groups. We also give a deformation of finite groups of Lie type by using their maximal abelian subgroups.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...