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arXiv · 1706.01279

On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra

Stéphane Launois·Omar León Sánchez
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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.

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Stéphane Launois, Omar León Sánchez. 2017-06-05. On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra. https://arxiv.org/abs/1706.01279

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