Cluster Algebras and Quiver Grassmannians

Cluster Algebras and Quiver Grassmannians

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Kyungyong Lee, University of Connecticut
Fine Hall 322

A cluster algebra, which was introduced by Fomin and Zelevinsky, is a commutative algebra with a family of distinguished generators (the cluster variables) grouped into overlapping subsets (the clusters) which are constructed by mutations. A quiver Grassmannian is a projective variety parametrizing subrepresentations of a quiver representation with a given dimension vector. After introducing how cluster algebras are related to the Euler characteristics of quiver Grassmannians, we give explicit expressions for the Euler characteristics in the rank 2 case.