We show that the representation type of the Jacobian algebra P(Q, S) associated to a 2-acyclic quiver Q with non degenerate potential S is invariant under QP-mutations. We prove that, apart from very few exceptions, P(Q, S) is of tame representation type if and only if Q is of finite mutation type. We also show that most quivers Q of finite mutation type admit only one non-degenerate potential up to weak right equivalence. In this case, the isomorphism class of P(Q, S) depends only on Q and not on S. (C) 2015 Published by Elsevier Inc.
The representation type of Jacobian algebras
Labardini Fragoso, D.;
2016
Abstract
We show that the representation type of the Jacobian algebra P(Q, S) associated to a 2-acyclic quiver Q with non degenerate potential S is invariant under QP-mutations. We prove that, apart from very few exceptions, P(Q, S) is of tame representation type if and only if Q is of finite mutation type. We also show that most quivers Q of finite mutation type admit only one non-degenerate potential up to weak right equivalence. In this case, the isomorphism class of P(Q, S) depends only on Q and not on S. (C) 2015 Published by Elsevier Inc.
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