Cyclic contractions of dimer algebras always exist

30 Oct 2017  ·  Beil Charlie ·

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

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Rings and Algebras