Iyama, Osamu; Nakajima, Yusuke On steady non-commutative crepant resolutions. (English) Zbl 1419.16012 J. Noncommut. Geom. 12, No. 2, 457-471 (2018). Summary: We introduce special classes of non-commutative crepant resolutions (= NCCR) which we call steady and splitting. We show that a singularity has a steady splitting NCCR if and only if it is a quotient singularity by a finite abelian group. We apply our results to toric singularities and dimer models. Cited in 2 ReviewsCited in 5 Documents MSC: 16G50 Cohen-Macaulay modules in associative algebras 14A22 Noncommutative algebraic geometry 14E15 Global theory and resolution of singularities (algebro-geometric aspects) Keywords:non-commutative crepant resolutions; class groups; quotient singularities PDF BibTeX XML Cite \textit{O. Iyama} and \textit{Y. Nakajima}, J. Noncommut. Geom. 12, No. 2, 457--471 (2018; Zbl 1419.16012) Full Text: DOI arXiv