Deformation quantization using groupoids. Case of toric manifolds
Cadet, Frederic
arXiv, 0305261 / Harvested from arXiv
In the framework of C*-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes' tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel's noncommutative torus, and even Landi's noncommutative 4-sphere. We construct such groupoid for a wide class of T^n-spaces, that generalizes the one given for C^n by Bellissard and Vittot. In particular, using the geometric properties of the moment map discovered in the '80s by Atiyah, Delzant, Guillemin and Sternberg, it provides a \cstar-algebraic deformation quantization for all toric manifolds, including the 2-sphere and all complex projective spaces.
Publié le : 2003-05-18
Classification:  Mathematics - Operator Algebras,  Mathematical Physics,  46L65,  46LXX,  52D17,  53D20
@article{0305261,
     author = {Cadet, Frederic},
     title = {Deformation quantization using groupoids. Case of toric manifolds},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305261}
}
Cadet, Frederic. Deformation quantization using groupoids. Case of toric manifolds. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305261/