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arXiv · 0804.3813

Mutation of cluster-tilting objects and potentials

Aslak Bakke Buan·Osamu Iyama·Idun Reiten·David Smith
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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.

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Aslak Bakke Buan, Osamu Iyama, Idun Reiten, David Smith. 2011-04-25. Mutation of cluster-tilting objects and potentials. https://arxiv.org/abs/0804.3813

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