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 …

Let $ Z $ be the center of a nonnoetherian dimer algebra $ A $ on a torus. We show that the
nilradical $\operatorname {nil} Z $ of $ Z $ is prime, may be nonzero, and consists precisely …

Cyclic Contractions of Dimer Algebras Always Exist Page 1 https://doi.org/10.1007/s10468-018-9812-6
Cyclic Contractions of Dimer Algebras Always Exist Charlie Beil1 Received: 27 March 2017 …

Let Z be the center of a nonnoetherian dimer algebra on a torus. Although Z itself is also
nonnoetherian, we show that it has Krull dimension 3, and is locally noetherian on an open …

Noetherian dimer algebras form a prominent class of examples of noncommutative crepant
resolutions (NCCRs). However, dimer algebras that are noetherian are quite rare, and we …

We study a new class of quiver algebras on surfaces, called'geodesic ghor algebras'. These
algebras generalize cancellative dimer algebras on a torus to higher genus surfaces, where …

Dimer tree algebras are a class of non-commutative Gorenstein algebras of Gorenstein
dimension 1. In previous work we showed that the stable category of Cohen-Macaulay …

Abstract Let ψ: A→ A′ be a cyclic contraction of dimer algebras, with A non-cancellative
and A′ cancellative. A′ is then prime, noetherian, and a finitely generated module over its …

In this note we consider a notion of relative Frobenius pairs of commutative rings S/R. To
such a pair, we associate an N-graded R-algebra Π R (S) which has a simple description …

Dimer models are a combinatorial tool to describe certain algebras that appear as
noncommutative crepant resolutions of toric Gorenstein singularities. Unfortunately, not …