Maximal Green Sequences of Exceptional Finite Mutation Type Quivers


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Seven A. İ.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.10, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10
  • Publication Date: 2014
  • Doi Number: 10.3842/sigma.2014.089
  • Title of Journal : SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
  • Keywords: skew-symmetrizable matrices, maximal green sequences, mutation classes

Abstract

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.