English

Symmetric operads of GK-dimension one

Rings and Algebras 2026-04-14 v1

Abstract

We prove that there is no finitely generated symmetric operad of Gelfand-Kirillov dimension strictly between 1 and 2 that answers an open question posted in 2020. We also classify finitely generated prime symmetric operads of Gelfand-Kirillov dimension 1.

Keywords

Cite

@article{arxiv.2604.11469,
  title  = {Symmetric operads of GK-dimension one},
  author = {Yu Li and Zihao Qi and Yongjun Xu and James J. Zhang and Zerui Zhang and Xiangui Zhao},
  journal= {arXiv preprint arXiv:2604.11469},
  year   = {2026}
}