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Abstract:
Recent work by Buan, Marsh, Reiten, Todorov ... shows that
the Fomin-Zelevinsky cluster algebra associated with an
acyclic quiver is closely related to a certain triangulated
2-Calabi-Yau category constructed from its representations:
the cluster category. We show how to characterize this
category among (algebraic) 2-Calabi-Yau categories. We
present applications to the combinatorics of quiver
mutation and to the classification of Cohen-Macaulay
modules over certain singularities.
(Joint work with Idun Reiten)
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