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arXiv · 2010.12172

Growth of nonsymmetric operads

Zihao Qi·Yongjun Xu·James J. Zhang·Xiangui Zhao
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Abstract

The paper concerns the Gelfand-Kirillov dimension and the generating series of nonsymmetric operads. An analogue of Bergman's gap theorem is proved, namely, no finitely generated locally finite nonsymmetric operad has Gelfand-Kirillov dimension strictly between $1$ and $2$. For every $r\in \{0\}\cup \{1\}\cup [2,\infty)$ or $r=\infty$, we construct a single-element generated nonsymmetric operad with Gelfand-Kirillov dimension $r$. We also provide counterexamples to two expectations of Khoroshkin and Piontkovski about the generating series of operads.

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Zihao Qi, Yongjun Xu, James J. Zhang, Xiangui Zhao. 2023-06-04. Growth of nonsymmetric operads. https://doi.org/10.1512/iumj.2023.72.9243

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