非阿贝尔群型Nichols代数的维数与Hilbert级数的整除关系
Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type
摘要：
给出了一类非阿贝尔群型Nichols代数的维数和Hilbert级数的整除关系，推广了Coxeter群上具有常数上圈-1的Nichols代数.为此，我们引入了三组作用在Nichols代数上的同构，推广了Milinski和Schneider在“Coxeter群上的点不可分解霍普夫代数”中引入的Coxeter群的交换算子.
英文摘要：
We present a divisibility relation for the dimensions and Hilbert series of certain classes of Nichols algebras of non-abelian group type, which generalizes Nichols algebras over Coxeter groups with constant cocycle -1. For this we introduce three groups of isomorphisms acting on Nichols algebras, which generalize the exchange operator introduced by Milinski and Schneider for Coxeter groups in "Pointed indecomposable Hopf algebras over Coxeter groups".
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