TY - JOUR
T1 - Quivers with additive labelings
T2 - Classification and algebraic entropy
AU - Galashin, Pavel
AU - Pylyavskyy, Pavlo
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly sub- additive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to each quiver with an addi- tive 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.
AB - We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly sub- additive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to each quiver with an addi- tive 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.
KW - Arnold-Liouville integrability
KW - Cluster algebras
KW - T-system
KW - Twisted dynkin diagrams
KW - Zamolodchikov periodicity
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U2 - 10.25537/dm.2019v24.2057-2135
DO - 10.25537/dm.2019v24.2057-2135
M3 - Article
AN - SCOPUS:85078014513
VL - 24
SP - 2057
EP - 2135
JO - Documenta Mathematica
JF - Documenta Mathematica
SN - 1431-0635
ER -