PreprintCC0arXiv
Linear bounds and sharp exponential growth for commuting matrix algebra
Abstract
For any m pairwise commuting matrices {Ai}i=1m⊂ Mn(F), we prove dimF F[A1,⋯, Am]≤ (2m−1)(n−1)+1, answering Bergman's question on the existence of a linear bound for a fixed number m.
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BibTeX
@misc{li2026linear,
title = {{Linear bounds and sharp exponential growth for commuting matrix algebra}},
author = {Jiamei Li and Caihua Luo and Xu Song and Yilin Zeng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08135},
eprint = {2611.08135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08135},
note = {CC0},
}
RIS
TY - UNPB
TI - Linear bounds and sharp exponential growth for commuting matrix algebra
AU - Jiamei Li
AU - Caihua Luo
AU - Xu Song
AU - Yilin Zeng
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08135
UR - https://arxiv.org/abs/2611.08135
AB - For any m pairwise commuting matrices {A_i}_i=1^m⊂ M_n(F), we prove dim_F F[A_1,⋯, A_m]≤ (2^m−1)(n−1)+1, answering Bergman's question on the existence of a linear bound for a fixed number m.
ER -