Enveloping algebras of double Poisson-Ore extensions

ABSTRACT

It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under iterated double Ore extensions are invariants of the Poisson enveloping algebra of a double Poisson-Ore extension.

KEYWORDS:

• Double Ore extension
• double Poisson-Ore extension
• Poisson enveloping algebra

2010 Mathematics Subject Classification:

• 17B63
• 16S10

Acknowledgments

The authors would appreciate a referee for informing references [4] and [5] while it is revised.