Hochschild cohomology and Atiyah classes

DOI10.1016/j.aim.2010.01.012zbMath1197.14017arXiv0708.2725OpenAlexW2008218939MaRDI QIDQ981619

Michel Van den Bergh, Damien Calaque

Publication date: 1 July 2010

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

Full work available at URL: https://arxiv.org/abs/0708.2725

zbMATH Keywords

Hochschild cohomologydeformation quantizationLie algebroidAtiyah classpoly-differential operatorspoly-vector fields

Mathematics Subject Classification ID

Related Items (50)

On Lie algebroid over algebraic spaces ⋮ On the geometric interpretation of certain vertex algebras and their modules ⋮ Formality theorem for \(\mathfrak{g}\)-manifolds ⋮ The Kontsevich weight of a wheel with spokes pointing outward ⋮ The Stokes groupoids ⋮ Formality theorems for Hochschild complexes and their applications ⋮ Duality features of left Hopf algebroids ⋮ \(\Lambda\)-modules and holomorphic Lie algebroid connections ⋮ Geometry of localized effective theories, exact semi-classical approximation and the algebraic index ⋮ Noncommutative del Pezzo surfaces and Calabi-Yau algebras ⋮ ATIYAH CLASS AND CHERN CHARACTER FOR GLOBAL MATRIX FACTORISATIONS ⋮ The Gauss-Manin connection on the periodic cyclic homology ⋮ A PBW theorem for inclusions of (sheaves of) Lie algebroids ⋮ Hodge theory and derived categories of cubic fourfolds ⋮ Atiyah classes and dg-Lie algebroids for matched pairs ⋮ Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields ⋮ Derived equivalences of hyperkähler varieties ⋮ Atiyah classes and Todd classes of pullback dg Lie algebroids associated with Lie pairs ⋮ The orbifold Hochschild product for Fermat hypersurface ⋮ Hochschild cohomology of generalised Grassmannians ⋮ Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism ⋮ Remarks on derived equivalences of Ricci-flat manifolds ⋮ From Atiyah classes to homotopy Leibniz algebras ⋮ Deformation quantization and the action of Poisson vector fields ⋮ Formality theorem for differential graded manifolds ⋮ Polyvector fields for Fano 3-folds ⋮ Localization of Atiyah classes ⋮ Căldăraru's conjecture and Tsygan's formality ⋮ The multiplicative structure on Hochschild cohomology of a complete intersection ⋮ Deformation Quantization of Commutative Families and Vector Fields ⋮ The Ext algebra of a quantized cycle ⋮ The module structure of Hochschild homology in some examples ⋮ The algebraic index theorem and deformation quantization of Lagrange-Finsler and Einstein spaces ⋮ On the Lie algebroid of a derived self-intersection ⋮ Weak quantization of Poisson structures ⋮ A motivic global Torelli theorem for isogenous \(K3\) surfaces ⋮ The cyclic theory of Hopf algebroids. ⋮ A note on a question of Markman ⋮ Hopf algebras arising from dg manifolds ⋮ Derived equivalences of K3 surfaces and orientation ⋮ Derived geometry of the first formal neighbourhood of a smooth analytic cycle ⋮ One-dimensional Chern-Simons theory and the \(\widehat{A}\) genus ⋮ Remarks on the derived center of small quantum groups ⋮ The Hochschild cohomology ring of a global quotient orbifold ⋮ Todd class via homotopy perturbation theory ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ Hochschild cohomology of dg manifolds associated to integrable distributions ⋮ Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids. ⋮ Duality functors for quantum groupoids

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