广义Taft代数与对合对
Generalised Taft algebras and pairs in involution
摘要：
研究了一类有限维霍普夫代数，它推广了Taft代数的概念.给出了这些霍普夫代数在对合中省略一对的充要条件，即不具有类群和实现对极平方的特征标.作为结果，我们证明了有限维霍普夫代数的例子没有这样的对的无限集的存在性。这对反Yetter-Drinfeld模理论以及霍普夫代数表示的双对偶性都有影响。这篇文章已被接受发表在代数通信，由泰勒和弗朗西斯出版。
英文摘要：
A class of finite-dimensional Hopf algebras which generalise the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a pair in involution, that is, to not have a group-like and a character implementing the square of the antipode. As a consequence we prove the existence of an infinite set of examples of finite-dimensional Hopf algebras without such pairs. This has implications for the theory of anti-Yetter-Drinfeld modules as well as biduality of representations of Hopf algebras. This article has been accepted for publication in Communications in Algebra, published by Taylor & Francis.
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