Poisson algebras via model theory and differential-algebraic geometry

DOI10.4171/JEMS/712zbMath1416.17010arXiv1406.0867WikidataQ115212361 ScholiaQ115212361MaRDI QIDQ2359444

Rahim Moosa, Jason P. Bell, Omar León Sánchez, Stephane Launois

Publication date: 28 June 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.0867

zbMATH Keywords

model theoryPoisson algebrasprimitive idealDixmier-Moeglin equivalencedifferential algebraic geometryManin kernel

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Poisson algebras (17B63) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Differential algebra (12H05) Applications of model theory (03C98) Localization and associative Noetherian rings (16P50)

Related Items (23)

INVARIANT HYPERSURFACES ⋮ \(D\)-groups and the Dixmier-Moeglin equivalence ⋮ Commutative bidifferential algebra ⋮ Poisson structures on finitary incidence algebras ⋮ The Poisson spectrum of the symmetric algebra of the Virasoro algebra ⋮ A conjecture strengthening the Zariski dense orbit problem for birational maps of dynamical degree one ⋮ Cluster algebra structures on Poisson nilpotent algebras ⋮ The Dixmier-Moeglin equivalence for extensions of scalars and Ore extensions ⋮ The algebraic and geometric classification of transposed Poisson algebras ⋮ Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras ⋮ Transposed Poisson structures on Lie incidence algebras ⋮ A NEW FAMILY OF POISSON ALGEBRAS AND THEIR DEFORMATIONS ⋮ Isolated types of finite rank: an abstract Dixmier-Moeglin equivalence ⋮ On the Dixmier-Moeglin equivalence for Poisson-Hopf algebras ⋮ On the importance of being primitive ⋮ On extension of classical Baer results to Poisson algebras ⋮ A strong Dixmier-Moeglin equivalence for quantum Schubert cells ⋮ The orbit method for locally nilpotent infinite-dimensional Lie algebras ⋮ Poisson Dixmier-Moeglin equivalence from a topological point of view ⋮ The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra ⋮ Hopf algebra actions and rational ideals ⋮ The algebraic classification and degenerations of nilpotent Poisson algebras ⋮ Finiteness theorems on hypersurfaces in partial differential-algebraic geometry

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