Geodesic
NONNOETHERIAN HOMOTOPY DIMER ALGEBRAS AND NONCOMMUTATIVE CREPANT RESOLUTIONS
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 447-479

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DOI

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 consider the question: how close are nonnoetherian homotopy dimer algebras to being NCCRs? To address this question, we introduce a generalization of NCCRs to nonnoetherian tiled matrix rings. We show that if a noetherian dimer algebra is obtained from a nonnoetherian homotopy dimer algebra A by contracting each arrow whose head has indegree 1, then A is a noncommutative desingularization of its nonnoetherian centre. Furthermore, if any two arrows whose tails have indegree 1 are coprime, then A is a nonnoetherian NCCR. 
BEIL, CHARLIE. NONNOETHERIAN HOMOTOPY DIMER ALGEBRAS AND NONCOMMUTATIVE CREPANT RESOLUTIONS. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 447-479. doi: 10.1017/S0017089517000209
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     author = {BEIL, CHARLIE},
     title = {NONNOETHERIAN {HOMOTOPY} {DIMER} {ALGEBRAS} {AND} {NONCOMMUTATIVE} {CREPANT} {RESOLUTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {447--479},
     year = {2018},
     volume = {60},
     number = {2},
     doi = {10.1017/S0017089517000209},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000209/}
}
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