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Cluster-tilted algebras

Aslak Bakke Buan·Bethany Marsh·Idun Reiten
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Abstract

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.

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Aslak Bakke Buan, Bethany Marsh, Idun Reiten. 2004-02-05. Cluster-tilted algebras. https://arxiv.org/abs/math/0402075

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