From Atiyah classes to homotopy Leibniz algebras

DOI10.1007/s00220-015-2494-6zbMath1395.53090arXiv1204.1075OpenAlexW1937059200WikidataQ122875464 ScholiaQ122875464MaRDI QIDQ906916

Mathieu Stiénon, Ping Xu, Zhuo Chen

Publication date: 1 February 2016

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

Full work available at URL: https://arxiv.org/abs/1204.1075

Mathematics Subject Classification ID

Homological methods in Lie (super)algebras (17B55) Poisson manifolds; Poisson groupoids and algebroids (53D17) Local cohomology of analytic spaces (32C36)

Related Items (26)

Formality theorem for \(\mathfrak{g}\)-manifolds ⋮ Modular class of Lie \(\infty\)-algebroids and adjoint representations ⋮ Shifted derived Poisson manifolds associated with Lie pairs ⋮ Atiyah classes and dg-Lie algebroids for matched pairs ⋮ Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields ⋮ Atiyah classes and Todd classes of pullback dg Lie algebroids associated with Lie pairs ⋮ Crossed modules and non-abelian extensions of Rota-Baxter Leibniz algebras ⋮ Atiyah and Todd classes of regular Lie algebroids ⋮ The Atiyah class of generalized holomorphic vector bundles ⋮ Fedosov dg manifolds associated with Lie pairs ⋮ A Hopf algebra associated with a Lie pair ⋮ Atiyah and Todd classes arising from integrable distributions ⋮ Characteristic classes of Higgs bundles and Reznikov's theorem ⋮ Exponential map and \(L_{\infty}\) algebra associated to a Lie pair ⋮ Rozansky-Witten-type invariants from symplectic Lie pairs ⋮ Hopf algebras arising from dg manifolds ⋮ Poincaré-Birkhoff-Witt isomorphisms and Kapranov dg-manifolds ⋮ Bicrossed products induced by Poisson vector fields and their integrability ⋮ One-dimensional Chern-Simons theory and the \(\widehat{A}\) genus ⋮ Invariant connections and PBW theorem for Lie groupoid pairs ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs ⋮ Lie-Rinehart algebras \(\simeq\) acyclic Lie \(\infty \)-algebroids ⋮ Atiyah classes and Kontsevich–Duflo type theorem for dg manifolds ⋮ Polyvector fields and polydifferential operators associated with Lie pairs ⋮ Hochschild cohomology of dg manifolds associated to integrable distributions ⋮ Dg manifolds, formal exponential maps and homotopy Lie algebras

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