Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 007, 8 pages      arXiv:1712.08478      https://doi.org/10.3842/SIGMA.2020.007
Contribution to the Special Issue on Cluster Algebras

Some Consequences of Categorification

Dylan Rupel a and Salvatore Stella b
a)  Pasadena Unified School District, Math Academy, Pasadena, CA 91101, USA
b)  Università degli studi di Roma ''La Sapienza'', Dipartimento di Matematica ''G. Castelnuovo'', P.le Aldo Moro, 5 - 00185 Rome, Italy

Received October 16, 2019, in final form January 21, 2020; Published online January 30, 2020

Abstract
Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomin-Zelevinsky, Reading-Speyer, and Reading-Stella related to $\mathbf{d}$-vectors, $\mathbf{g}$-vectors, and $F$-polynomials.

Key words: acyclc cluster algebras; categorification; valued quivers.

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