Cluster-tilted algebras

Bakke Buan, Aslak; Marsh, Bethany; Reiten, Idun

doi:10.1090/S0002-9947-06-03879-7

Cluster-tilted algebras
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by Aslak Bakke Buan, Bethany R. Marsh and Idun Reiten PDF

Trans. Amer. Math. Soc. 359 (2007), 323-332

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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