English

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 4040 infinite families and 1313 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

R2 v1 2026-06-22T19:19:14.480Z