Locally anti de Sitter spaces and deformation quantization

Details Locally anti de Sitter spaces and deformation quantization Locally anti de Sitter spaces and deformation quantization

2009-12-11

arxiv.org/abs/0912.2215v1

Mathematics

Differential Geometry

123 pages, PhD. thesis

Scientific paper

In the first part we define a "BTZ" black hole in anti de Sitter space in any dimension by defining as "singular" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the appendix, most of the notions about homogeneous spaces and Iwasawa decompositions that are needed. Explicit matricial decompositions are given for every Lie algebra that will be used in the thesis: sl(2,R), so(1,n), so(2,n), sl(2,C) and sp(2,R).

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