Period 2 quivers and their T- and Y-systems
Mathematical Physics
2021-09-24 v1 Commutative Algebra
Dynamical Systems
math.MP
Abstract
We give a general definition for period quivers before making some prudent assumptions to reduce the number of possibilities. Finding these quivers requires solving a complicated system of equations between the number of arrows in the quiver. We find all solutions of these systems for quivers with vertices and give some solutions for . We then consider the - and -systems associated with these quivers, some of which exhibit periodic quantities which lead to reductions; in a few cases we obtain the Somos-4 and Somos-5 recurrences.
Cite
@article{arxiv.2109.11107,
title = {Period 2 quivers and their T- and Y-systems},
author = {Joe Pallister},
journal= {arXiv preprint arXiv:2109.11107},
year = {2021}
}