Quivers with additive labelings: classification and algebraic entropy
Combinatorics
2017-05-11 v2 Mathematical Physics
math.MP
Representation Theory
Abstract
We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly subadditive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to each quiver with an additive labeling, we completely classify such quivers, obtaining infinite families and exceptional quivers. This completes the program of classifying Zamolodchikov periodic and integrable quivers.
Cite
@article{arxiv.1704.05024,
title = {Quivers with additive labelings: classification and algebraic entropy},
author = {Pavel Galashin and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:1704.05024},
year = {2017}
}
Comments
77 pages, 29 figures; v2: some references, remarks, and support information added