Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2057-2135 |
| Number of pages | 79 |
| Journal | Documenta Mathematica |
| Volume | 24 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© Deutsche Mathematiker Vereinigung.
Keywords
- Arnold-Liouville integrability
- Cluster algebras
- T-system
- Twisted dynkin diagrams
- Zamolodchikov periodicity