Cohomology structure for a Poisson algebra:Ⅱ

作者：Yan-Hong Bao; Yu Ye^*

来源：Science China Mathematics, 2021, 64(05): 903-920.

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.

• 单位
  安徽大学; 中国科学技术大学