A Dixmier-Moeglin equivalence for Poisson algebras with torus actions

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dc.creatorGoodearl, K. R.
dc.date2005-12-22
dc.date.accessioned2026-07-07T06:55:40Z
dc.date.available2026-07-07T06:55:40Z
dc.descriptionA Poisson analog of the Dixmier-Moeglin equivalence is established for any affine Poisson algebra $R$ on which an algebraic torus $H$ acts rationally, by Poisson automorphisms, such that $R$ has only finitely many prime Poisson $H$-stable ideals. In this setting, an additional characterization of the Poisson primitive ideals of $R$ is obtained -- they are precisely the prime Poisson ideals maximal in their $H$-strata (where two prime Poisson ideals are in the same $H$-stratum if the intersections of their $H$-orbits coincide). Further, the Zariski topology on the space of Poisson primitive ideals of $R$ agrees with the quotient topology induced by the natural surjection from the maximal ideal space of $R$ onto the Poisson primitive ideal space. These theorems apply to many Poisson algebras arising from quantum groups. The full structure of a Poisson algebra is not necessary for the results of this paper, which are developed in the setting of a commutative algebra equipped with a set of derivations.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0512514
dc.identifierhttp://arxiv.org/abs/math/0512514
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106353
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject17B63; 13N15
dc.titleA Dixmier-Moeglin equivalence for Poisson algebras with torus actions
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