The classification of Nichols algebras over groups with finite root system of rank two
The classification of Nichols algebras over groups with finite root system of rank two
复制标题
有限二阶根系群上尼科尔斯代数的分类
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
L. Vendramin
中科院分区：
文献类型：
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作者：
I. Heckenberger;L. Vendramin
我们对G上的所有群G和绝对单Yetter-Drinfeld模的所有对(V，W)进行分类，使得V和W的直和的支撑生成G，V和W之间的辫子的平方不是恒等式，并且V和W的直和的Nichols代数允许有限的根系统.作为副产品，我们确定了这类Nichols代数的维度，得到了几类新的有限维Nichols代数。我们的主要工具是群上绝对简单的Yetter-Drinfeld模对的Weyl群胚。
We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols algebra of the direct sum of V and W admits a finite root system. As a byproduct, we determine the dimensions of such Nichols algebras, and several new families of finite-dimensional Nichols algebras are obtained. Our main tool is the Weyl groupoid of pairs of absolutely simple Yetter-Drinfeld modules over groups.