REVIEW 8 cited by
Deformation quantization of Poisson manifolds, I
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Deformation quantization of Poisson manifolds, I
read the original abstract
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the set of equivalence classes of Poisson structures on X modulo diffeomorphisms. In fact, a more general statement is proven ("Formality conjecture"), relating the Lie superalgebra of polyvector fields on X and the Hochschild complex of the algebra of functions on X. Coefficients in explicit formulas for the deformed product can be interpreted as correlators in a topological open string theory, although I do not use explicitly the language of functional integrals. One of corollaries is a justification of the orbit method in the representation theory.
Forward citations
Cited by 8 Pith papers
-
Quantization of Gravity on Null Hypersurfaces
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
-
Problem of Time and Background Independence: classical version's higher Lie Theory
Extends classical Lie theory with Lie's Algorithm and a commuting pentagon invariance criterion to locally resolve the Problem of Time via background independence.
-
A-type Sigma Models from Differential Poisson Geometry
Symplectic reduction of the differential Poisson sigma model yields a restricted class of classical A-type models whose quartic curvature coupling is induced by torsion of a flat connection, with the Kodaira–Thurston ...
-
Flows on Graded Manifolds
Defines flows on Z-graded manifolds and proves unique maximal flows for vector fields under stated conditions.
-
Covariant phase space approach to noncommutativity in tensile and tensionless open strings
Covariant phase space analysis shows tensionless open strings in constant Kalb-Ramond background have purely boundary-supported phase space with noncommutative endpoint coordinates, recovering Seiberg-Witten noncommut...
-
How to have your wormholes and factorize, too
A modified semiclassical holographic dictionary is used to construct an extended gravitational path integral that factorizes, reproduces the Page curve for entropy, and includes operators for baby universe states.
-
Chaos and epoch structure in the deformed Mixmaster universe
GUP deformation shortens Kasner epochs in the Mixmaster universe while polymerization lengthens them, with combined effects adding linearly and chaos strength depending on the deformation parameters.
-
Q-Manifolds and Sigma Models
The paper summarizes BV formalism using Q- and QP-manifolds and constructs BV action functionals from the geometry of Lie algebroids and Courant algebroids.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.