Formality theorems for Hochschild chains in the Lie algebroid setting

DOI10.1515/CRELLE.2007.085zbMath1141.53084arXivmath/0504372MaRDI QIDQ5459210

Gilles Halbout, Damien Calaque, Vasiliy A. Dolgushev

Publication date: 25 April 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504372

zbMATH Keywords

resolutionLie algebroidformality theoremsHochschild cochainsquantum traces

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Deformation quantization, star products (53D55) Differential graded algebras and applications (associative algebraic aspects) (16E45) Cohomology of Lie (super)algebras (17B56)

Related Items (17)

\(\Lambda\)-modules and holomorphic Lie algebroid connections ⋮ Atiyah classes and dg-Lie algebroids for matched pairs ⋮ Lie bialgebroid of pseudo-differential operators ⋮ Formality of differential graded algebras and complex Lagrangian submanifolds ⋮ Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism ⋮ Formality theorem for differential graded manifolds ⋮ Căldăraru's conjecture and Tsygan's formality ⋮ On global deformation quantization in the algebraic case ⋮ Formality theorem with coefficients in a module ⋮ Weak quantization of Poisson structures ⋮ Hochschild cohomology and Atiyah classes ⋮ \(L_\infty \)-resolutions and twisting in the curved context ⋮ LIE ALGEBROIDS AS SPACES ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ Deformation quantization in algebraic geometry ⋮ The strong homotopy structure of Poisson reduction

Cites Work

• Covariant and equivariant formality theorems
• Characteristic classes of gauge systems
• Closed star products and cyclic cohomology
• Déformation du crochet de Poisson sur une variété symplectique
• Pseudodifferential operators on differential groupoids
• A proof of the Tsygan formality conjecture for chains.
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
• Deformation quantization with traces
• Lie algebroids, holonomy and characteristic classes
• Deformation quantization of Poisson manifolds
• The cohomology structure of an associative ring
• Formality for Lie algebroids
• Deformation quantization in algebraic geometry
• Differential Forms On Regular Affine Algebras
• Pseudodifferential calculus on manifolds with corners and groupoids
• Differential Forms on General Commutative Algebras
• Quantum groupoids
• Cyclic formality and index theorem
• Deformation quantization of algebraic varieties.

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