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.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- September 2017
- DOI:
- 10.1007/s11005-017-0967-6
- arXiv:
- arXiv:1608.00172
- Bibcode:
- 2017LMaPh.107.1715L
- Keywords:
-
- Mathematics - Rings and Algebras;
- 16E40;
- 17B35;
- 17B63
- E-Print:
- 26 pages, any comment is welcome