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arXiv · 1608.00172

Homological unimodularity and Calabi-Yau condition for Poisson algebras

Jiafeng Lü·Xingting Wang·Guangbin Zhuang
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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.

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Jiafeng Lü, Xingting Wang, Guangbin Zhuang. 2016-07-30. Homological unimodularity and Calabi-Yau condition for Poisson algebras. https://doi.org/10.1007/s11005-017-0967-6

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