Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras

DOI10.5802/aif.1624zbMath0973.17027arXivmath/0010039OpenAlexW2316006980MaRDI QIDQ1266220

Johannes Huebschmann

Publication date: 14 September 1998

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010039

zbMATH Keywords

Poisson structuresBatalin-Vilkovisky algebrasLie-Rinehart algebrasabstract left and right connectionscohomological duality for Lie-Rinehart algebrasGertenhaber algebras

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Homological methods in Lie (super)algebras (17B55) Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63) Cohomology of Lie (super)algebras (17B56)

Related Items (53)

Homology and modular classes of Lie algebroids. ⋮ Divergence operators and odd Poisson brackets ⋮ The BV formalism for \(L_\infty \)-algebras ⋮ Cohomologies and crossed modules for pre-Lie Rinehart algebras ⋮ A Lie–Rinehart Algebra with No Antipode ⋮ Quasi-Bigèbres de Lie et Algèbres Quasi-Batalin-Vilkovisky Différentielles ⋮ Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras ⋮ On 3-Hom-Lie-Rinehart algebras ⋮ Equivalence relation on differential quasi-Batalin-Vilkovisky algebras ⋮ Universal central extensions of Lie–Rinehart algebras ⋮ Braided Cartan calculi and submanifold algebras ⋮ Hom-Lie-Rinehart algebras ⋮ On duality between étale groupoids and Hopf algebroids ⋮ Poisson geometry ⋮ Poisson structures on trivial extension algebras ⋮ Hochschild (co)homologies of DG \(K\)-algebras and their Koszul duals ⋮ Unnamed Item ⋮ Graded Lie-Rinehart algebras ⋮ ACTIONS OF MONOIDAL CATEGORIES AND REPRESENTATIONS OF CARTAN TYPE LIE ALGEBRAS ⋮ Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories ⋮ Toward differentiation and integration between Hopf algebroids and Lie algebroids ⋮ Representations of Homotopy Lie–Rinehart Algebras ⋮ Batalin-Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras ⋮ Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology ⋮ Invariants of Lie algebroids ⋮ OPERADIC APPROACH TO COHOMOLOGY OF ASSOCIATIVE TRIPLE AND N-TUPLE SYSTEMS ⋮ Poisson cohomology of plane Poisson structures with isolated singularities revisited ⋮ Differential calculus on Jordan algebras and Jordan modules ⋮ On (co-)morphisms of Lie pseudoalgebras and groupoids ⋮ On Hom-Lie–Rinehart Algebras ⋮ BV-GENERATORS AND LIE ALGEBROIDS ⋮ Split Lie–Rinehart algebras ⋮ Structure and cohomology of 3-Lie-Rinehart superalgebras ⋮ The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation ⋮ Lie-Rinehart bialgebras for crossed products ⋮ Connections on modules over singularities of finite CM representation type ⋮ Duality and comparison for logarithmic de Rham complexes with respect to free divisors. ⋮ On Hom-Gerstenhaber algebras, and Hom-Lie algebroids ⋮ Kirillov structures up to homotopy ⋮ Deformation of hom-Lie-Rinehart algebras ⋮ On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras ⋮ Lie-Rinehart algebras \(\simeq\) acyclic Lie \(\infty \)-algebroids ⋮ The universal pre-Lie-Rinehart algebras of aromatic trees ⋮ Batalin-Vilkovisky structure on Hochschild cohomology of tame Hecke algebras of type \(\mathbf{A}\) ⋮ Lie algebroids, holonomy and characteristic classes ⋮ Lie groupoids and Lie algebroids in physics and noncommutative geometry ⋮ Deformation theory of Courant algebroids via the Rothstein algebra ⋮ On anchored Lie algebras and the Connes-Moscovici bialgebroid construction ⋮ Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids. ⋮ Star calculus on Jacobi manifolds. ⋮ Distributive laws between the Three Graces ⋮ Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor ⋮ Formal solution of the master equation via HPT and deformation theory

Cites Work

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• Differential homological algebra and homogeneous spaces
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• New perspectives on the BRST-algebraic structure of string theory
• The cohomology structure of an associative ring
• Relative Homological Algebra
• Poisson cohomology and quantization.
• Duality for Lie-Rinehart algebras and the modular class
• Transverse measures, the modular class and a cohomology pairing for Lie algebroids
• Differential Forms on General Commutative Algebras

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