From local to global deformation quantization of Poisson manifolds
By Alberto S. Cattaneo, Giovanni Felder, L. Tomassini. 2000
165 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/70bc96eb62dde93fb93335de86fb5f4bb02e7bfe
How researchers see this paper
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In Algebra and Number Theory
In Geometry and Topology
- Amnon Yekutieli
- M. Kontsevich
- M. Abouzaid
- Mark Gross
- Yukinobu Toda
- Michel van den Bergh
- T. Bridgeland
- Andrei Căldăraru
In Mathematical Physics
- Amnon Yekutieli
- M. Kontsevich
- M. Abouzaid
- Mark Gross
- Yukinobu Toda
- Michel van den Bergh
- T. Bridgeland
- Andrei Căldăraru
Citations in the corpus
- Bimodule deformations, picard groups and contravariant connections (2002, unknown): “ar X iv :m at h/ 02 07 25 5v”
- On the AKSZ Formulation of the Poisson Sigma Model (2001, unknown): “Q A ] 2 6 Fe b”
- Deformation quantization in algebraic geometry (2003, methodology): “L∞morphism between two DG Lie algebras is explained in [Ko1]. It is a “homomorphism of DG Lie algebras up to prescribed higher homotopies.” Here is a version of the L∞equations that was worked out in [CFT]: for all m1,...,mp,m∈ N, αj ∈ Vm j C[[t]]TC[[t]]/C and b0,...,bm ∈ C[[t]] one has (2.6) Xp l=0”
- Deformation Quantization of Algebraic Varieties (2001, background): “that there exists an L∞ quasi-isomorphism from Tpoly(X) to Dpoly(X) (see also [ CFT ] for a different approach, presumably equivalent to one in [Ko1]).”