Taft与Nichols Hopf代数在其基域上的部分（余）作用的分类

Taft与Nichols Hopf代数在代数上的部分（余）作用

Partial (co)actions of Taft and Nichols Hopf algebras on algebras

该研究刻画了Taft与Nichols Hopf代数在代数上的适宜部分（余）作用，证明其具有对称性，且特定代数的全部此类作用均被涵盖，推广了作者此前的相关研究成果。

Classification of PM Quiver Hopf Algebras

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$ is the complex field and $G$ is a finite abelian group, we classify quiver Hopf algebras over $G$, multiple Taft algebras over $G$ and Nichols algebras in $^{kG}_{kG} {\cal YD}$. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.

Classifying bicrossed products of two Taft algebras

We classify all Hopf algebras which factorize through two Taft algebras $\mathbb{T}_{n^{2}}(\bar{q})$ and respectively $T_{m^{2}}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\bar{q} \neq q^{n-1}$ then the matched pairs are in bijection with the group of $d$-th roots of unity in $k$, where $d = (m,\,n)$ while if $\bar{q} = q^{n-1}$ then besides the matched pairs above we obtain an additional family of matched pairs indexed by $k^{*}$. The corresponding bicrossed products (double cross product in Majid's terminology) are explicitly described by…

Taft代数在预投射代数上的作用

Taft algebra actions on preprojective algebras

本研究分类了广义Taft代数在A型扩展Dynkin箭图预投射代数上的作用，拓展了两变量多项式环作用分类问题，计算了类群元素旋转作用下的不变量，且证明特定情形下不变环与预投射代数中心同构。

Pointed Hopf actions on central simple division algebras

We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a division algebra. This is in contrast to earlier work of Etingof and Walton, in which it was shown that most pointed Hopf algebras do not admit faithful actions on fields. We consider all bosonizations of Nichols algebras of finite Cartan type, small quantum groups…