A differential graded Lie algebra controlling the Poisson deformations of an affine Poisson variety

摘要

We construct a differential graded Lie algebra controlling the Poisson deformations of an affine Poisson variety. We analyze in the case of affine Gorenstein toric Poisson varieties. Moreover, explicit description of the second and third Hochschild cohomology groups is given for three-dimensional affine Gorenstein toric varieties.