Maximal Green Sequences of Exceptional Finite Mutation Type Quivers

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2014-01-01

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Seven, Ahmet İrfan

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Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. The existence of maximal green sequences for exceptional finite mutation type quivers has been shown by Alim-Cecotti-Cordova-Espahbodi-Rastogi-Vafa except for the quiver X-7. In this paper we show that the quiver X-7 does not have any maximal green sequences. We also generalize the idea of the proof to give sufficient conditions for the non-existence of maximal green sequences for an arbitrary quiver.

Subject Keywords

Skew-symmetrizable matrices, Maximal green sequences, Mutation classes

URI

https://hdl.handle.net/11511/47545

Journal

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS

DOI

https://doi.org/10.3842/sigma.2014.089

Collections

Department of Mathematics, Article

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Citation Formats

A. İ. Seven, “Maximal Green Sequences of Exceptional Finite Mutation Type Quivers,” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, pp. 0–0, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47545.