Toric Poisson Ideals in Cluster Algebras

Sebastian Zwicknagl

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Toric Poisson Ideals in Cluster Algebras

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arxiv 1009.2936 v2 pith:LBNK6EIN submitted 2010-09-15 math.RT

Toric Poisson Ideals in Cluster Algebras

Sebastian Zwicknagl This is my paper

classification math.RT

keywords idealspoissonclusteralgebracompatiblemanytorusactions

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This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely many torus invariant Poisson prime ideals and we show how to obtain using the exchange matrix of an initial seed. In fact, these ideals are independent of the choice of compatible Poisson structure. In many interesting cases the ideals can be described more explicitly.

Toric Poisson Ideals in Cluster Algebras

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