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A Counterexample to Left-Right Symmetry for Diagonal Auslander-Regularity
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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BibTeX
@misc{wang2026counterexample,
title = {{A Counterexample to Left-Right Symmetry for Diagonal Auslander-Regularity}},
author = {Zhenyu Wang and Zhaoyong Huang and Yu-Zhe Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11406},
eprint = {2610.11406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11406},
}
RIS
TY - UNPB
TI - A Counterexample to Left-Right Symmetry for Diagonal Auslander-Regularity
AU - Zhenyu Wang
AU - Zhaoyong Huang
AU - Yu-Zhe Liu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11406
UR - https://arxiv.org/abs/2610.11406
AB - 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.
ER -