The generalized Weyl Poisson algebras and their Poisson simplicity criterion
Abstract
A new class of Poisson algebras, the class of 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.
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