Cyclic contractions of dimer algebras always exist

Abstract

We show that every nondegenerate dimer algebra $A$ on a torus admits a cyclic contraction to a cancellative dimer algebra. This implies, for example, that $A$ is Calabi-Yau if and only if it is noetherian; and that the center of $A$ has Krull dimension $3$.

20 pages

References in corpus (5)

• Dimer models and cluster categories of Grassmannians
• A Dimer ABC
• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• Cancellativization of dimer models
• On steady non-commutative crepant resolutions