Universal enveloping algebras of Poisson Ore extensions

DOI10.1090/S0002-9939-2015-12631-7zbMath1378.16034arXiv1403.5852OpenAlexW1975824997MaRDI QIDQ2944839

Xingting Wang, Guangbin Zhuang, Jia Feng Lü

Publication date: 8 September 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5852

zbMATH Keywords

universal enveloping algebraPoisson algebraOre extension

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Poisson algebras (17B63) Universal enveloping algebras of Lie algebras (16S30)

Related Items (13)

DG Poisson algebra and its universal enveloping algebra ⋮ The Nakayama automorphism of a class of graded algebras ⋮ The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras ⋮ Homological unimodularity and Calabi-Yau condition for Poisson algebras ⋮ Reflection groups and rigidity of quadratic Poisson algebras ⋮ The Zariski cancellation problem for Poisson algebras ⋮ Universal enveloping algebras of generalized Poisson-Ore extensions ⋮ PBW-basis for universal enveloping algebras of differential graded Poisson algebras ⋮ Realization of Poisson enveloping algebra ⋮ Enveloping algebras of double Poisson-Ore extensions ⋮ Poisson Dixmier-Moeglin equivalence from a topological point of view ⋮ Poisson double extensions ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Universal enveloping algebras and universal derivations of Poisson algebras
• Normal forms for orthogonal similarity classes of skew-symmetric matrices
• Double Ore extensions.
• Universal enveloping algebras of Poisson Hopf algebras
• A quadratic Poisson Gel’fand-Kirillov problem in prime characteristic
• Double Ore Extensions Versus Iterated Ore Extensions
• The Dixmier-Moeglin equivalence and a Gel’fand-Kirillov problem for Poisson polynomial algebras
• Poisson cohomology and quantization.
• Poisson enveloping algebras
• Poisson orders, symplectic reflection algebras and representation theory
• The Yoneda Algebra of a Graded Ore Extension
• Poisson Polynomial Rings

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