2005/12/22 by K. R. Goodearl, Goodearl, K. R.
Mathematics · #13N15 #17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:13N15 #msc:17B63
paper · pdf · doi:10.48550/arxiv.math/0512514
25 pages
arxiv created 2005/12/22 · openalex publication_date 2005/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 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.