The generalized Weyl Poisson algebras and their Poisson simplicity criterion

Abstract

A new large 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 an explicit description of the Poisson centre is obtained. Many examples are considered (e.g. the classical polynomial Poisson algebra in 2n variables is a generalized Weyl Poisson algebra).

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Item Type:	Article
Authors/Creators:	Bavula, V.V.
Copyright, Publisher and Additional Information:	© The Author(s) 2019. Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords:	A generalized Weyl Poisson algebra; A Poisson algebra; The Poisson centre; A Poisson prime ideal; The Poisson simplicity
Dates:	Accepted: 4 September 2019 Published (online): 27 September 2019 Published: January 2020
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Symplectic Sheffield
Date Deposited:	13 May 2019 10:13
Last Modified:	28 Sep 2020 16:26
Status:	Published
Publisher:	Springer
Refereed:	Yes
Identification Number:	10.1007/s11005-019-01214-7
Related URLs:	arXiv URL
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:145799

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The generalized Weyl Poisson algebras and their Poisson simplicity criterion

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