The generalized Weyl Poisson algebras and their Poisson simplicity criterion

Abstract

A new class of Poisson algebras, the class of {\em generalized Weyl Poisson algebras}, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras and explicit descriptions of the Poisson centre and the absolute Poisson centre are obtained. Many examples are considered.

12 pages

Cited by in corpus (2)

• Automorphism groups of deformations and quantizations of Kleinian singularities
• Ideals in enveloping algebras of affine Kac-Moody algebras