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- Title
Homological unimodularity and Calabi-Yau condition for Poisson algebras.
- Authors
Lü, Jiafeng; Wang, Xingting; Zhuang, Guangbin
- 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.
- Subjects
HOMOLOGY theory; CALABI-Yau manifolds; POISSON algebras; PICARD groups; DUALITY theory (Mathematics)
- Publication
Letters in Mathematical Physics, 2017, Vol 107, Issue 9, p1715
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-017-0967-6