Twisted Poincaré duality between Poisson homology and Poisson cohomology

DOI10.1016/j.jalgebra.2014.08.023zbMath1392.17015arXiv1404.5177OpenAlexW2963244089MaRDI QIDQ493012

Yong-Cai Geng, Sumit K. Garg

Publication date: 11 September 2015

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

Full work available at URL: https://arxiv.org/abs/1404.5177

zbMATH Keywords

modular classPoincaré dualityPoisson algebrasPoisson (co)homology

Mathematics Subject Classification ID

Homological methods in Lie (super)algebras (17B55) Poisson algebras (17B63) Duality in applied homological algebra and category theory (aspects of algebraic topology) (55U30)

Related Items (12)

Cohomology structure for a Poisson algebra. II ⋮ Co-Poisson structures on polynomial Hopf algebras ⋮ Homological unimodularity and Calabi-Yau condition for Poisson algebras ⋮ Modular derivations for extensions of Poisson algebras ⋮ Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry ⋮ Reflection groups and rigidity of quadratic Poisson algebras ⋮ A note on the duality between Poisson homology and cohomology ⋮ Nakayama automorphisms and modular derivations in filtered deformations ⋮ Poisson double extensions ⋮ Frobenius Poisson algebras ⋮ Cohomologies of \textsf{PoiMod} pairs and compatible structures on Poisson algebras ⋮ Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras

Cites Work

• Unnamed Item
• Noncommutative del Pezzo surfaces and Calabi-Yau algebras
• Homological properties of certain generalized Jacobian Poisson structures in dimension 3
• Poisson (co)homology of polynomial Poisson algebras in dimension four: Sklyanin's case
• Calabi-Yau algebras viewed as deformations of Poisson algebras.
• On the Hochschild homology of elliptic Sklyanin algebras.
• The Van den Bergh duality and the modular symmetry of a Poisson variety
• A differential complex for Poisson manifolds
• Les variétés de Poisson et leurs algèbres de Lie associees
• Gerstenhaber algebras and BV-algebras in Poisson geometry
• Noncommutative homology of some three-dimensional quantum spaces
• The modular automorphism group of a Poisson manifold
• The rigid dualizing complex of a universal enveloping algebra
• Formal Poisson cohomology of quadratic Poisson structures
• Poisson cohomology of the affine plane
• Homologies of cubic Artin-Schelter regular algebras
• Twisted Poincaré duality for some quadratic Poisson algebras
• Poisson (co)homology and isolated singularities
• POISSON STRUCTURES: TOWARDS A CLASSIFICATION
• On one class of exact Poisson structures
• Poisson cohomology and quantization.
• Poisson enveloping algebras
• Duality for Lie-Rinehart algebras and the modular class

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