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On steady non-commutative crepant resolutions. (English) Zbl 1419.16012
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.

MSC:
16G50 Cohen-Macaulay modules in associative algebras
14A22 Noncommutative algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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