Abstract
For a Poisson algebra, we prove that the Poisson cohomology theory introduced by Flato et al. (1995) is given by a certain derived functor. We show that the (generalized) deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild conditions. Finally we construct a long exact sequence, and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11401001, 11871071, 11431010 and 11571329).
11401001,11871071,11431010 and 11571329).
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Bao, YH., Ye, Y. Cohomology structure for a Poisson algebra: II. Sci. China Math. 64, 903–920 (2021). https://doi.org/10.1007/s11425-019-1591-6
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DOI: https://doi.org/10.1007/s11425-019-1591-6