A Counterexample to Left-Right Symmetry for Diagonal Auslander-Regularity
Zhenyu Wang, Zhaoyong Huang, Yu-Zhe Liu
Abstract
We construct a finite-dimensional Auslander-regular algebra R with global dimension three, which is right diagonal but not left diagonal; moreover, any simple right R-module with grade i has projective dimension i, but there is a simple left R-module with grade one and projective dimension two. It answers a question raised by Iyama negatively.
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