Mutation of cluster-tilting objects and potentials

Details Mutation of cluster-tilting objects and potentials Mutation of cluster-tilting objects and potentials

2008-04-23

arxiv.org/abs/0804.3813v4

Mathematics

Representation Theory

41 pages. In the previous version, there was a mistake in the proof of old Theorem 5.1 asserting compatibility of mutation of

Scientific paper

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.

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