Algebras and Representation Theory

, Volume 22, Issue 5, pp 1083–1100 | Cite as

Cyclic Contractions of Dimer Algebras Always Exist

  • Charlie BeilEmail author
Open Access


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.


Dimer algebra Dimer model Noncommutative algebraic geometry Non-noetherian ring 

Mathematics Subject Classification (2010)

13C15 14A20 



Open access funding provided by Austrian Science Fund (FWF). The author would like to thank Akira Ishii, Kazushi Ueda, and Ana Garcia Elsener for useful discussions, as well as an anonymous referee for comments that have helped improve the article. The author was supported by the Austrian Science Fund (FWF) grant P 30549-N26.


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institut für Mathematik und Wissenschaftliches RechnenUniversität GrazGrazAustria

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