Submission date: 5 June 2017

Abstract:

We prove that the Poisson version of the Dixmier-Moeglin equivalence holds for cocommutative affine Poisson-Hopf algebras. This is a first step towards understanding the symplectic foliation and the representation theory of (cocommutative) affine Poisson-Hopf algebras. Our proof makes substantial use of the model theory of fields equipped with finitely many possibly noncommuting derivations. As an application, we show that the symmetric algebra of a finite dimensional Lie algebra, equipped with its natural Poisson structure, satisfies the Poisson Dixmier-Moeglin equivalence.

Mathematics Subject Classification: 17B63, 03C98, 12H05, 16T05

Keywords and phrases: Dixmier-Moeglin equivalence, Poisson-Hopf algebras, model theory of differential fields

Full text arXiv 1706.01279: pdf, ps.