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arXiv · 1606.00938

Cluster-tilted and quasi-tilted algebras

Ibrahim Assem·Ralf Schiffler·Khrystyna Serhiyenko
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Abstract

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so that any two local slices can be reached one from the other by a sequence of reflections and coreflections. We then give an algorithmic procedure for constructing the tubes of a cluster-tilted algebra of euclidean type. Our main result characterizes quasi-tilted algebras whose relation-extensions are cluster-tilted of euclidean type.

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Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko. 2016-06-03. Cluster-tilted and quasi-tilted algebras. https://arxiv.org/abs/1606.00938

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