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Maximal rigid objects as noncrossing bipartite graphs (1111.2306v1)
Published 9 Nov 2011 in math.RT and math.CO
Abstract: Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid objects in the corresponding orbit category C(Q), in terms of bipartite noncrossing graphs (with loops) in a circle. We also describe the endomorphism algebras of the maximal rigid objects, and we prove that a certain class of these algebras are iterated tilted algebras of type A.