Lie-Rinehart algebras \(\simeq\) acyclic Lie \(\infty \)-algebroids

DOI10.1016/j.jalgebra.2021.11.023zbMath1482.18016arXiv2106.13458OpenAlexW4200036339WikidataQ115465588 ScholiaQ115465588MaRDI QIDQ2068124

Camille Laurent-Gengoux, Ruben Louis

Publication date: 19 January 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.13458

zbMATH Keywords

Lie algebroidsalgebraic geometrysingular foliationsLie-Rinehart algebrasalgebras up to homotopyLie infinity algebras

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Poisson manifolds; Poisson groupoids and algebroids (53D17) Foliations (differential geometric aspects) (53C12) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Higher categories and homotopical algebra (18N99)

Related Items (5)

The holonomy of a singular leaf ⋮ Modular class of Lie \(\infty\)-algebroids and adjoint representations ⋮ The modular class of a singular foliation ⋮ On symmetries of singular foliations ⋮ Keller admissible triples and Duflo theorem

Cites Work

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• On the category of Lie \(n\)-algebroids
• Twisted differential string and fivebrane structures
• Derived brackets
• Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
• BV formality
• From Atiyah classes to homotopy Leibniz algebras
• Distributions involutives singulieres
• Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
• Introduction to sh Lie algebras for physicists
• Holonomy groupoids of singular foliations.
• Deformation quantization of Poisson manifolds
• Poincaré-Birkhoff-Witt isomorphisms and Kapranov dg-manifolds
• The universal Lie \(\infty\)-algebroid of a singular foliation
• Smoothness of holonomy covers for singular foliations and essential isotropy
• Higher derived brackets and homotopy algebras
• Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves
• Integrating Lie algebroids via stacks
• Rozansky-Witten invariants via Atiyah classes
• $Q$-manifolds and Higher Analogs of Lie Algebroids
• Homotopy equivalence of shifted cotangent bundles
• On the strong homotopy associative algebra of a foliation
• Representations of Homotopy Lie–Rinehart Algebras
• Integration of Differential Graded Manifolds
• Homotopy Rinehart cohomology of homotopy Lie-Rinehart pairs
• A homotopy Lie-Rinehart resolution and classical BRST cohomology

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