Equivariant quantization of orbifolds

Journal of Geometry and Physics - Tập 60 - Trang 1103-1111 - 2010
N. Poncin1, F. Radoux2, R. Wolak3
1University of Luxembourg, Campus Limpertsberg, Mathematics Research Unit, 162A, avenue de la Faïencerie, L-1511 Luxembourg City, Luxembourg
2University of Liège, Institute of Mathematics, Grande Traverse, 12 - B37, B-4000 Liège, Belgium
3Jagiellonian University, ulica Reymonta 4 30-059 Krakow, Poland

Tài liệu tham khảo

Lecomte, 1996, Comparison of some modules of the Lie algebra of vector fields, Indag. Math., 7, 461, 10.1016/S0019-3577(97)89133-1 Lecomte, 1999, Projectively equivariant symbol calculus, Lett. Math. Phys., 49, 173, 10.1023/A:1007662702470 Duval, 1999, Conformally equivariant quantization: existence and uniqueness, Ann. Inst. Fourier, 49, 1999, 10.5802/aif.1744 Lecomte, 2000, On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol, Indag. Math., 11, 95, 10.1016/S0019-3577(00)88577-8 Boniver, 2001, Maximal subalgebras of vector fields for equivariant quantizations, J. Math. Phys., 42, 582, 10.1063/1.1332782 Duval, 2001, Projectively equivariant quantization and symbol calculus: noncommutative hypergeometric functions, Lett. Math. Phys., 57, 61, 10.1023/A:1017954812000 Boniver, 2002, Equivariant symbol calculus for differential operators acting on forms, Lett. Math. Phys., 62, 219, 10.1023/A:1022251607566 Boniver, 2006, IFFT-equivariant quantizations, J. Geom. Phys., 56, 712, 10.1016/j.geomphys.2005.04.014 M. Bordemann, Sur l’existence d’une prescription d’ordre naturelle projectivement invariante. arXiv:math.DG/0208171. Mathonet, 2005, Natural and projectively equivariant quantizations by means of Cartan connections, Lett. Math. Phys., 72, 183, 10.1007/s11005-005-6783-4 Hansoul, 2007, Existence of natural and projectively equivariant quantizations, Adv. Math., 214, 832, 10.1016/j.aim.2007.03.007 Bordemann, 2007 J. Huebschmann, Quantization and reduction. ArXiv:math/0207166. J. Huebschmann, Classical phase space singularities and quantization. ArXiv:math-ph/0610047v1. J. Huebschmann, G. Rudolph, M. Schmidt, A gauge model for quantum mechanics on a stratified space. ArXiv:hep-th/0702017. L. Hui, Singular unitary in quantization commutes with reduction. ArXiv:0706.1471. Pflaum, 2003, On the deformation quantization of symplectic orbispaces, Differential Geom. Appl., 19, 343, 10.1016/S0926-2245(03)00050-0 Girbau, 1983, On deformations of transversely holomorphic foliations, J. Reine Angew. Math., 345, 22 Poncin, 2009, A first approximation for quantization of singular spaces, J. Geom. Phys., 59, 503, 10.1016/j.geomphys.2009.01.002