论文标题
非对称作业的生长
Growth of nonsymmetric operads
论文作者
论文摘要
该论文涉及Gelfand-Kirillov维度和一系列非对称作业。证明了伯格曼差距定理的类似物，即，没有有限生成的本地非对称式出版物的Gelfand-Kirillov Dimension严格在$ 1 $和2美元之间。对于\ {0 \} \ cup \ {1 \} \ cup [2，\ infty）$或$ r = \ infty $的每一个$ r \，我们构建了一个与gelfand-kirillov dimension $ r $ r $的单一元素生成的非对称性作品。我们还为Khoroshkin和Piontkovski的两个期望提供了对生成一系列作业的期望。
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.
