dc.contributor.author | Neshveyev, Sergey | en_US |
dc.contributor.author | Tuset, Lars | en_US |
dc.date.accessioned | 2013-03-07T09:56:38Z | |
dc.date.available | 2013-03-07T09:56:38Z | |
dc.date.issued | 2012-03-01 | en_US |
dc.identifier.citation | Neshveyev, S. & Tuset, L. (2012). Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers. Communications in Mathematical Physics 312(1) | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.other | FRIDAID 941258 | en_US |
dc.identifier.uri | https://hdl.handle.net/10642/1381 | |
dc.description.abstract | Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 < q < 1. We study a quantization C(G q /K q ) of the algebra of continuous functions on G/K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C(G q /K q ) and obtain a composition series for C(G q /K q ). We describe closures of the symplectic leaves of G/K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C(G q /K q ). Next we show that the family of C*-algebras C(G q /K q ), 0 < q ≤ 1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra . Finally, extending a result of Nagy, we show that C(G q /K q ) is canonically KK-equivalent to C(G/K). | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.subject | VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Statistikk: 412 | en_US |
dc.subject | VDP::Matematikk og Naturvitenskap: 400::Fysikk: 430 | en_US |
dc.subject | Statistical physics | en_US |
dc.subject | Dynamical systems | en_US |
dc.subject | Complexity | en_US |
dc.subject | Quantum physics | en_US |
dc.subject | Mathematical physics | en_US |
dc.title | Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | Postprint title varies from published title. The original publication is available at www.springerlink.com | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s00220-012-1455-6 | |