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...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11401001,11871071,11431010 and 11571329)。
文摘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.
