Deformation Quantization of Commutative Families and Vector Fields

DOI10.1007/978-3-030-34072-8_11zbMath1442.81039OpenAlexW2989687103MaRDI QIDQ3294710

Georgy I. Sharygin

Publication date: 29 June 2020

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-34072-8_11

zbMATH Keywords

Poisson geometrydeformation quantization and star-productsLie algebras actions

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Deformations of general structures on manifolds (58H15) Deformation quantization, star products (53D55) Symplectic aspects of Floer homology and cohomology (53D40)

Cites Work

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• A new cohomology theory associated to deformations of Lie algebra morphisms
• Covariant and equivariant formality theorems
• Hochschild cohomology and Atiyah classes
• Deformation quantization and the action of Poisson vector fields
• Deformation quantization of Poisson manifolds
• Deformation quantization of integrable systems
• Survey of the deformation quantization of commutative families
• Classical and quantum integrability
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM

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