论文标题
有限的GK维尼科尔斯对角线类型和有限根系的代数
Finite GK-dimensional Nichols algebras of diagonal type and finite root systems
论文作者
论文摘要
令$（v，c）$为对角线类型的有限维编织矢量空间。我们表明，nichols代数$ \ mathfrak {b}（v）$的Gelfand Kirillov尺寸是有限的，并且仅当相应的根系是有限的，即$ \ Mathfrak {b}（v）$允许使用有限的发电机数量的PBW基础。 这是在Arxiv中猜想的：1606.02521，并以$ \ dim v = 2,3 $在ARXIV中证明：1803.08804，Arxiv：2106.10143。
Let $(V,c)$ be a finite-dimensional braided vector space of diagonal type. We show that the Gelfand Kirillov dimension of the Nichols algebra $\mathfrak{B}(V)$ is finite if and only if the corresponding root system is finite, that is $\mathfrak{B}(V)$ admits a PBW basis with a finite number of generators. This had been conjectured in arXiv:1606.02521 and proved for $\dim V=2,3$ in arXiv:1803.08804, arXiv:2106.10143 respectively.
