Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.10, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 10
- Publication Date: 2014
- Doi Number: 10.3842/sigma.2014.089
- Journal Name: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: skew-symmetrizable matrices, maximal green sequences, mutation classes
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
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.