The representation type of Jacobian algebras
By C. Geiss, Daniel Labardini-Fragoso, J. Schröer. 2013
74 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/15188f7e8a3ee2caa7500468d1ca6d39a8998e78
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In Geometry and Topology
In Molecular Biology
In Statistical and Nonlinear Physics
Citations in the corpus
- Quiver algebras as Fukaya categories (2013, background): “lomorphic, cf. Remarks 3.22 and 4.14. The constraint on the number of punctures |M| > max{3,g+ 1} when S is closed arises from a similar constraint in work of Geiss, Labardini-Fragoso and Schro¨er [17], who study the action of right equivalences on potentials on the quivers Q(T), cf. Theorem 2.1.”
- Cluster categories for marked surfaces: punctured case (2013, background): “3.3 the Jacobian algebra P(QT,WT) is a skew-gentle algebra for an admissible triangulation T of a marked surface. This result was first announced by Labardini-Fragoso (cf. [25]) and was first proved in [15]. 3.2. Correspondences. Denote by rep(QT,WT) the category of finite dimensional k-linear represen”