A Dixmier-Moeglin equivalence for Poisson algebras with torus actions

Details A Dixmier-Moeglin equivalence for Poisson algebras with torus actions A Dixmier-Moeglin equivalence for Poisson algebras with torus actions

2005-12-22

arxiv.org/abs/math/0512514v1

Mathematics

Representation Theory

25 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A Dixmier-Moeglin equivalence for Poisson algebras with torus actions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Dixmier-Moeglin equivalence for Poisson algebras with torus actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Dixmier-Moeglin equivalence for Poisson algebras with torus actions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726324