Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces

Details Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces Quantized anti de Sitter spaces and non-formal deformation quantizations of symplectic symmetric spaces

2007-05-29

arxiv.org/abs/0705.4179v1

Mathematics

Quantum Algebra

24 pages, to appear in Contemporary Mathematics (AMS) in the volume of the proceedings of the conference Poisson 2006 held at

Scientific paper

We realize quantized anti de Sitter space black holes, building Connes spectral triples, similar to those used for quantized spheres but based on Universal Deformation Quantization Formulas (UDF) obtained from an oscillatory integral kernel on an appropriate symplectic symmetric space. More precisely we first obtain a UDF for Lie subgroups acting on a symplectic symmetric space M in a locally simply transitive manner. Then, observing that a curvature contraction canonically relates anti de Sitter geometry to the geometry of symplectic symmetric spaces, we use that UDF to define what we call Dirac-isospectral noncommutative deformations of the spectral triples of locally anti de Sitter black holes. The study is motivated by physical and cosmological considerations.

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