Cluster-tilted algebras
Representation Theory
2020-12-21 v2 Rings and Algebras
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.
Cite
@article{arxiv.math/0402075,
title = {Cluster-tilted algebras},
author = {Aslak Bakke Buan and Bethany Marsh and Idun Reiten},
journal= {arXiv preprint arXiv:math/0402075},
year = {2020}
}
Comments
12 pages. Extra reference included in introduction; rest of paper unchanged