Cyclic Contractions of Dimer Algebras Always Exist
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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.
KeywordsDimer 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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