Quivers with additive labelings: classification and algebraic entropy

2017/04/17 by Pavel Galashin, Galashin, Pavel, Pavlo Pylyavskyy +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #05E99 (Secondary) #13F60 (Primary) #37K10 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum many-body systems #Representation Theory (math.RT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1704.05024

openalex publication_date 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 40 infinite families and 13 exceptional quivers. This completes the program of classifying Zamolodchikov periodic and integrable quivers.

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