Symmetric operads of GK-dimension one
Yu Li, Zihao Qi, Yongjun Xu, James J. Zhang, Zerui Zhang, and Xiangui Zhao
TL;DR
This paper proves the non-existence of certain finitely generated symmetric operads with Gelfand-Kirillov dimension between 1 and 2 and classifies prime symmetric operads with dimension 1.
Contribution
It resolves an open question from 2020 by establishing non-existence results and provides a classification for prime symmetric operads of GK-dimension 1.
Findings
No finitely generated symmetric operad of GK-dimension between 1 and 2 exists.
Finitely generated prime symmetric operads of GK-dimension 1 are classified.
The paper answers an open question in the field.
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.
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