The algebraic index theorem and deformation quantization of Lagrange-Finsler and Einstein spaces

DOI10.1063/1.4815977zbMath1287.83042arXiv1005.3647OpenAlexW3100902283MaRDI QIDQ5407614

Sergiu I. Vacaru

Publication date: 7 April 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3647

zbMATH Keywords

deformation quantizationHochschild homologyEinstein spacealgebraic index theoremalmost Kähler/Poisson structuresLagrange-Finsler

Mathematics Subject Classification ID

(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Quantization of the gravitational field (83C45) Geometry and quantization, symplectic methods (81S10) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Deformation quantization, star products (53D55) Kähler-Einstein manifolds (32Q20) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (5)

On supersymmetric geometric flows and \(\mathcal R^2\) inflation from scale invariant supergravity ⋮ Nonholonomic jet deformations, exact solutions for modified Ricci soliton and Einstein equations ⋮ Heterotic supergravity with internal almost-Kähler spaces; instantons for SO (32), or E ₈ × E ₈ , gauge groups; and deformed black holes with soliton, quasiperiodic and/or pattern-forming structures ⋮ (para-) Kähler structures on \(\rho \)-commutative algebras ⋮ Effective Einstein cosmological spaces for non-minimal modified gravity

Cites Work

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• Hochschild cohomology of the Weyl algebra and traces in deformation quantization
• Deformation quantization of nonholonomic almost Kähler models and Einstein gravity
• A simple algebraic proof of the algebraic index theorem
• On general solutions for field equations in Einstein and higher dimension gravity
• Hochschild cohomology and Atiyah classes
• Einstein gravity in almost Kähler and Lagrange-Finsler variables and deformation quantization
• Symplectic curvatue tensors
• Fedosov manifolds
• Operads and motives in deformation quantization
• A simple geometrical construction of deformation quantization
• On the dequantization of Fedosov's deformation quantization
• Riemann-Roch theorems via deformation quantization. I
• Deformation quantization of Poisson manifolds
• Algebraic index theorem
• \(\mathcal W\) geometry from Fedosov's deformation quantization
• The index of elliptic operators. I
• Formal symplectic groupoid of a deformation quantization
• Lagrange–Fedosov nonholonomic manifolds
• FINSLER AND LAGRANGE GEOMETRIES IN EINSTEIN AND STRING GRAVITY
• Deformation quantization of almost Kähler models and Lagrange-Finsler spaces
• NONHOLONOMIC DISTRIBUTIONS AND GAUGE MODELS OF EINSTEIN GRAVITY
• BRANES AND QUANTIZATION FOR AN A-MODEL COMPLEXIFICATION OF EINSTEIN GRAVITY IN ALMOST KÄHLER VARIABLES
• Fedosov quantization of Lagrange–Finsler and Hamilton–Cartan spaces and Einstein gravity lifts on (co) tangent bundles
• The Spectral Theory of Toeplitz Operators. (AM-99)
• Lagrange geometry
• The classification of spaces defining gravitational fields
• Fedosov deformation quantization as a BRST theory
• Almost-Kähler deformation quantization.

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