Cohomology structure for a Poisson algebra: II

  • Yan-Hong Bao
  • Yu YeEmail author


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.


Poisson algebra Poisson cohomology formal deformation deformation quantization 


16E40 16W10 17B37 


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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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesAnhui UniversityHefeiChina
  2. 2.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  3. 3.Wu Wen-Tsun Key Laboratory of MathematicsUSTC, Chinese Academy of SciencesHefeiChina

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