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 $Γ= End_A(M)$, where $M$ is a reflexive $A$-module, $Γ$ is maximal Cohen-Macaulay as an $A$-module and $gldim(Γ)_P = \dim A_P $ 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.