Noetherian criteria for dimer algebras

Abstract

Let $A$ be a nondegenerate dimer (or ghor) algebra on a torus, and let $Z$ be its center. Using cyclic contractions, we show the following are equivalent: $A$ is noetherian; $Z$ is noetherian; $A$ is a noncommutative crepant resolution; each arrow of $A$ is contained in a perfect matching whose complement supports a simple module; and the vertex corner rings $e_{i}A{e}_i$ are pairwise isomorphic.

20 pages. Replaces part of arXiv:1412.1750, with new results. Fixed problem of figures not displaying properly in the PDF of v2

References in corpus (1)

• A note on consistency conditions on dimer models

Cited by in corpus (3)

• Dimer algebras, ghor algebras, and cyclic contractions
• Spacetime geometry of spin, polarization, and wavefunction collapse
• A generalization of cancellative dimer algebras to hyperbolic surfaces