Fedosov quantization in algebraic context
By R. Bezrukavnikov, D. Kaledin. 2003
130 citations recorded by the source corpus.
We consider the problem of quantization of smooth symplectic varieties in the algebro-geometric setting. We show that, under appropriate cohomological assumptions, the Fedosov quantization procedure goes through with minimal changes. The assumptions are satisfied, for example, for affine and for projective varieties. We also give a classification of all possible quantizations.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f797748144bc5fee16444413ded08aaafcb2754
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Ben Webster
- Damien Calaque
- I. Losev
- Michel van den Bergh
- Tudor Dimofte
- D. Gaiotto
- Mathew Bullimore
- Alex Weekes
In Geometry and Topology
- Ben Webster
- Michel van den Bergh
- Tudor Dimofte
- I. Losev
- D. Gaiotto
- Damien Calaque
- Mathew Bullimore
- Amnon Yekutieli
In Mathematical Physics
- Damien Calaque
- Ben Webster
- Michel van den Bergh
- Tudor Dimofte
- I. Losev
- D. Gaiotto
- Mathew Bullimore
- Amnon Yekutieli
Citations in the corpus
- Quantized symplectic actions and W -algebras (2007, background): “Since the second de Rham cohomology of X is trivial, the existence of a G-equivariant isomorphism W ∼ = D(G, e) is derived from standard results on the equivalence of star-products; see [ BeKa ] or [GR], for example.”
- Deformation quantization of gerbes (2005, unknown): “also [3] for the algebraic case).”
- Hochschild cohomology and Atiyah classes (2007, methodology): “Algebraic versions of formal geometry were introduced independently and around the same time by Bezrukavikov and Kaledin in [2] and Yekutieli in [40].”
- Deformation quantization in algebraic geometry (2003, background): “Finally, let us mention several recent papers and surveys dealing with deformation quantization: [ BK1 ,BK2,CDH,CF,CI,Do1,Do2,Ke].”
- Yangians and quantizations of slices in the affine Grassmannian (2012, methodology): “The most relevant work for us is [Bezrukavnikov and Kaledin 2004], showing the existence and uniqueness of deformation quantizations of symplectic resolutions.”
- The Coulomb Branch of 3d N = 4 Theories (2015, background): “The types of spaces that arise as Higgs and Coulomb branches of a 3d N = 4 gauge theory possess the required “nice” properties as long the branches can be fully resolved by turning on mass and FI parameters [38], cf.”