论文标题
可分解的HOPF代数的伴随稳定代数的结构
Structures of Adjoint-Stable Algebras over Factorizable Hopf Algebras
论文作者
论文摘要
对于Quasi三角形Hopf代数$ \ left（h，r \ right）$，有一个由Majid引入的Transmuted编织组$ h_ {r} $ $ h $的概念。 Transmuted编织组$ H_ {R} $是编织类别中的Hopf代数$ _ {H} \ Mathcal {M} $。与任何简单的左$ h_ {r} $ - comodule相关联的$ r $ - adjoint-stable代数是由作者定义的，用于表征所有不可约蛋的结构，$ {} _ {} _ {h} _ {h}^{h}^{h}^{h}^{h}^{h} \ mathcal {yd} $ {在本说明中，我们证明了一个半神经的可置换hopf代数$ \ left（h，r \右）$，任何简单的$ h_r $的subcoalgebra is $ h_r $ is $ h $ stable和$ r $ r $ -Adjoint-stable代数用于任何简单的左$ H_R $ h_r $ -comodule is anti-isomorphic is anti-Isomorphic to $ h $ $ h $。作为一个应用程序，我们表征了所有不可还原的Yetter-Drinfeld模块。
For a quasi-triangular Hopf algebra $\left( H,R\right) $, there is a notion of transmuted braided group $H_{R}$ of $H$ introduced by Majid. The transmuted braided group $H_{R}$ is a Hopf algebra in the braided category $_{H}\mathcal{M}$. The $R$-adjoint-stable algebra associated with any simple left $H_{R}$-comodule is defined by the authors, and is used to characterize the structure of all irreducible Yetter-Drinfeld modules in ${}_{H}^{H} \mathcal{YD}$. In this note, we prove for a semisimple factorizable Hopf algebra $ \left( H,R\right) $ that any simple subcoalgebra of $H_R$ is $H$-stable and the $R$-adjoint-stable algebra for any simple left $H_R$-comodule is anti-isomorphic to $H$. As an application, we characterize all irreducible Yetter-Drinfeld modules.
