Toric Poisson Ideals in Cluster Algebras

Sebastian Zwicknagel (U Bonn)

Wednesday 17th November, 2010 16:00-17:00 204


Cluster Algebras come equipped with a natural Poisson bracket, or potentially a family of Poisson brackets which are "related" via the actions of an algebraic torus. In this talk I will show how to classify the torus invariant Poisson prime ideals of a cluster algebra using the combinatorial data obtained from the exchange matrix. Finally I will apply this method to the case of the cluster algebra of functions on matrices. Of course, I will also introduce all the relevant notions.

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