Examples of non-commutative crepant resolutions of Cohen Macaulay normal domains

Abstract

Let A be a Cohen–Macaulay normal domain. A non-commutative crepant resolution (NCCR) of A is an A-algebra Γ of the form Γ=EndA(M), where M is a reflexive A-module, Γ is maximal Cohen–Macaulay as an A-module and gldim(Γ)P=dim⁡AP for all primes P of A. We give bountiful examples of equi-characteristic Cohen–Macaulay normal local domains and mixed characteristic Cohen–Macaulay normal local domains having NCCR. We also give plentiful examples of affine Cohen–Macaulay normal domains having NCCR.