On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra
Rings and Algebras
2017-11-10 v2
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.
Keywords
Cite
@article{arxiv.1706.01279,
title = {On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra},
author = {Stéphane Launois and Omar León Sánchez},
journal= {arXiv preprint arXiv:1706.01279},
year = {2017}
}