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Mutation of cluster-tilting objects and potentials
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| Venue: | Amer. Journal Math. (2008 |
| Citations: | 56 - 11 self |
BibTeX
@ARTICLE{Buan_mutationof,
author = {A. B. Buan and O. Iyama and I. Reiten and D. Smith},
title = {Mutation of cluster-tilting objects and potentials},
journal = {Amer. Journal Math. (2008},
year = {},
pages = {08043813}
}
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Abstract
Abstract. We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This gives a close connection between 2-CY-tilted algebras and Jacobian algebras associated with quivers with potentials. We show that cluster-tilted algebras are Jacobian and also that they are determined by their quivers. There are similar results when dealing with tilting modules over 3-CY algebras. The nearly Morita equivalence for 2-CY-tilted algebras is shown to hold for the finite length modules over Jacobian algebras.
