Universal enveloping algebras of Poisson Ore extensions

Abstract

We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As consequences, we observe certain ring-theoretic invariants of the universal enveloping algebras that are preserved under iterated Poisson-Ore extensions. We apply our results to iterated quadratic Poisson algebras arising from semiclassical limits of quantized coordinate rings and a family of graded Poisson algebras of Poisson structures of rank at most two.

13 pages

References in corpus (1)

• The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras

Cited by in corpus (9)

• Homological unimodularity and Calabi-Yau condition for Poisson algebras
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• The Zariski cancellation problem for Poisson algebras
• Reflection Groups and Rigidity of Quadratic Poisson Algebras
• Poisson Dixmier-Moeglin equivalence from a topological point of view
• Double Poisson extensions
• PBW-basis for universal enveloping algebras of differential graded Poisson algebras
• Universal enveloping algebras of differential graded Poisson algebras
• The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras