Maximal Green Sequences of Exceptional Finite Mutation Type Quivers


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Seven A. İ.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, cilt.10, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 10
  • Basım Tarihi: 2014
  • Doi Numarası: 10.3842/sigma.2014.089
  • Dergi Adı: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS

Özet

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.