Maximal green sequences of skew-symmetrizable 3x3 matrices
Combinatorics
2012-07-27 v1
Abstract
Maximal green sequences are particular sequences of mutations 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. In this paper, we show that skew-symmetrizable 3x3 matrices with a mutation-cyclic diagram do not have any maximal green sequences. We also obtain some properties of maximal green sequences of skew-symmetrizable 3x3 matrices with mutation-acyclic diagrams.
Keywords
Cite
@article{arxiv.1207.6265,
title = {Maximal green sequences of skew-symmetrizable 3x3 matrices},
author = {Ahmet Seven},
journal= {arXiv preprint arXiv:1207.6265},
year = {2012}
}
Comments
6pages