Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Combinatorics
2014-08-20 v3
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-C\'ordova-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-C\'ordova-Espahbodi-Rastogi-Vafa except for the quiver . In this paper we show that the quiver 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.
Keywords
Cite
@article{arxiv.1406.1072,
title = {Maximal Green Sequences of Exceptional Finite Mutation Type Quivers},
author = {Ahmet I. Seven},
journal= {arXiv preprint arXiv:1406.1072},
year = {2014}
}