Noncommutative homogeneous spaces: The matrix case

Metric Aspects of Noncommutative Homogeneous Spaces

For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism ρ : K̂ → G satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations C∗(Ĝ/Γ, ρ) of the homogeneous space G/Γ, generalizing Rieffel’s construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is conn...

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

The Noncommutative S-Matrix

As a simple example of how recently developed on-shell techniques apply to nonlocal theories, we study the S-matrix of noncommutative gauge theories. In the complex plane, this S-matrix has essential singularities that signal the nonlocal behavior of the theory. In spite of this, we show that tree-level amplitudes may be obtained by BCFW type recursion relations. At one loop we find a complete ...

Properly discontinuous groups on certain matrix homogeneous spaces

We characterize discrete groups Γ ⊂ GL(n,R) which act properly discontinuously on the homogeneous space GL(m,R)\GL(n,R).