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Mutation of cluster-tilting objects and potentials
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 4, August 2011
- pp. 835-887
- 10.1353/ajm.2011.0031
- Article
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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.