Cohomology structure for a Poisson algebra:Ⅱ

• 作者: Yan-Hong Bao Yu Ye
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: Articles
• 页码范围: 903-920
• 页数: 18页
• 语种: 英文

摘要

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.