Homological unimodularity and Calabi–Yau condition for Poisson algebras
Homological unimodularity and Calabi–Yau condition for Poisson algebras
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DOI：
10.1007/s11005-017-0967-6
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发表时间：
2016-07
影响因子：
1.2
通讯作者：
Jia-feng Lü;Xingting Wang;G. Zhuang
中科院分区：
文献类型：
--
作者：
Jia-feng Lü;Xingting Wang;G. Zhuang
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.
