Geodesic
Quivers with Additive Labelings: Classification and Algebraic Entropy
Documenta mathematica, Tome 24 (2019), pp. 2057-2135
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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.
DOI : 10.4171/dm/721
Classification : 05E99, 13F60, 37K10
Mots-clés : cluster algebras, Zamolodchikov periodicity, T-system, Arnold-Liouville integrability, twisted Dynkin diagrams 
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     author = {Pavel Galashin and Pavlo Pylyavskyy},
     title = {Quivers with {Additive} {Labelings:} {Classification} and {Algebraic} {Entropy}},
     journal = {Documenta mathematica},
     pages = {2057--2135},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/721},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/721/}
}
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Pavel Galashin; Pavlo Pylyavskyy. Quivers with Additive Labelings: Classification and Algebraic Entropy. Documenta mathematica, Tome 24 (2019), pp. 2057-2135. doi: 10.4171/dm/721

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