Homological unimodularity and Calabi-Yau condition for Poisson algebras

Abstract

In this paper, we show that the twisted Poincaré duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of a unimodular Poisson algebra in terms of its Poisson Picard group. We also achieve twisted Poincaré duality for Hochschild (co)homology of Poisson bimodules using rigid dualizing complex. For a smooth Poisson affine variety with the trivial canonical bundle, we prove that its enveloping algebra is a Calabi-Yau algebra if the Poisson structure is unimodular.

26 pages, any comment is welcome

References in corpus (5)

• Calabi-Yau algebras
• Universal enveloping algebras of Poisson Ore extensions
• Twisted Poincare duality for some quadratic Poisson algebras
• DG Poisson algebra and its universal enveloping algebra
• Maximal commutative subalgebras, Poisson geometry and Hochschild homology

Cited by in corpus (3)

• The Zariski cancellation problem for Poisson algebras
• Reflection Groups and Rigidity of Quadratic Poisson Algebras
• Duality for Differential Operators of Lie-Rinehart Algebras