From local to global deformation quantization of Poisson manifolds

被引：0
|
作者：
Cattaneo, AS [1 ]
Felder, G
Tomassini, L
机构：
[1] Univ Zurich, Math Inst, CH-8057 Zurich, Switzerland
[2] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland
来源：
DUKE MATHEMATICAL JOURNAL | 2002年 / 115卷 / 02期
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifold, based on M. Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.
引用
收藏
页码：329 / 352
页数：24
相关论文
共 50 条
  • [31] Causal Poisson bracket via deformation quantization
    Berra-Montiel, Jasel
    Molgado, Alberto
    Palacios-Garcia, Cesar D.
    [J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2016, 13 (07)
  • [32] Lectures on props, Poisson geometry and deformation quantization
    Merkulov, S. A.
    [J]. POISSON GEOMETRY IN MATHEMATICS AND PHYSICS, 2008, 450 : 223 - 257
  • [33] Cohomology and deformation quantization of Poisson conformal algebras
    Liu, Jiefeng
    Zhou, Hongyu
    [J]. JOURNAL OF ALGEBRA, 2023, 630 : 92 - 127
  • [34] Symplectic and Poisson derived geometry and deformation quantization
    Pantev, Tony
    Vezzosi, Gabriele
    [J]. ALGEBRAIC GEOMETRY: SALT LAKE CITY 2015, PT 2, 2018, 97 : 405 - 457
  • [35] Deformation quantization and the action of Poisson vector fields
    Sharygin G.
    [J]. Lobachevskii Journal of Mathematics, 2017, 38 (6) : 1093 - 1107
  • [36] Deformation quantization for almost-Kahler manifolds
    Schlichenmaier, M
    [J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 : 49 - 54
  • [37] Fock Representations and Deformation Quantization of Kahler Manifolds
    Sako, Akifumi
    Umetsu, Hiroshi
    [J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (03) : 2769 - 2794
  • [38] A universal formula for deformation quantization on Kahler manifolds
    Gammelgaard, Niels Leth
    [J]. ADVANCES IN MATHEMATICS, 2014, 259 : 766 - 783
  • [39] Deformation quantization modules on complex symplectic manifolds
    Schapira, Pierre
    [J]. POISSON GEOMETRY IN MATHEMATICS AND PHYSICS, 2008, 450 : 259 - 271
  • [40] Wick type deformation quantization of Fedosov manifolds
    Dolgushev, VA
    Lyakhovich, SL
    Sharapov, AA
    [J]. NUCLEAR PHYSICS B, 2001, 606 (03) : 647 - 672
12345