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The ozone groups of the algebras Bq(f)
Abstract
Let q be a primitive n-th root of unity, n>1, and let f be a nonzero polynomial such that nnmid(j+1) for every j∈supp(f). Set e=gcd(n,{j+1:j∈supp(f)}). We show that Oz(Bq(f))≅μe×μe: the defining relations are homogeneous for a ℤ/e×ℤ/e grading, the center sits in degree zero, and the ozone group is the character group of that grading. The determination of the ozone group only requires the central elements un, vn, and Ω. The regular normal elements modulo the center form the same group, generated by un/e and vn/e, so every normal element is central exactly when e=1. For f=t2 we recover a computation of Chan, Gaddis, Won and Zhang, and for e>1 we obtain an infinite family of Calabi--Yau algebras with nontrivial ozone group.
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BibTeX
@misc{gomez2026ozone,
title = {{The ozone groups of the algebras $B_q(f)$}},
author = {James Gómez and Helbert Venegas},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28868},
eprint = {2608.28868},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28868},
}
RIS
TY - UNPB
TI - The ozone groups of the algebras B_q(f)
AU - James Gómez
AU - Helbert Venegas
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28868
UR - https://arxiv.org/abs/2608.28868
AB - Let q be a primitive n-th root of unity, n>1, and let f be a nonzero polynomial such that nnmid(j+1) for every j∈supp(f). Set e=gcd(n,{j+1:j∈supp(f)}). We show that Oz(B_q(f))≅μ_e×μ_e: the defining relations are homogeneous for a ℤ/e×ℤ/e grading, the center sits in degree zero, and the ozone group is the character group of that grading. The determination of the ozone group only requires the central elements u^n, v^n, and Ω. The regular normal elements modulo the center form the same group, generated by u^n/e and v^n/e, so every normal element is central exactly when e=1. For f=t^2 we recover a computation of Chan, Gaddis, Won and Zhang, and for e>1 we obtain an infinite family of Calabi--Yau algebras with nontrivial ozone group.
ER -