论文标题
尖锐的Hopf代数（CO）对理性功能的行动
Pointed Hopf algebra (co)actions on rational functions
论文作者
论文摘要
本文介绍了在代数$ k $上作用于代数形态的hopf代数$ h $的构建。该方法特别适合控制这些动作是否限制在给定的$ k $的$ k $的$ h $，以及这些操作是否与$ k $上的给定$*$ - 结构兼容。该理论应用于包含坐标环$ b = k [t^2，t^3] $的有理函数的字段$ k = k（t）$。详细描述了一个明确的示例，并显示了尖端上定义量子均匀的空间结构，与先前已知的空间结构相比，该结构从常规函数延伸到合理函数。
This article studies the construction of Hopf algebras $H$ acting on a given algebra $K$ in terms of algebra morphisms $ σ\colon K \rightarrow \mathrm{M}_n(K)$. The approach is particularly suited for controlling whether these actions restrict to a given subalgebra $B$ of $K$, whether $H$ is pointed, and whether these actions are compatible with a given $*$-structure on $K$. The theory is applied to the field $K=k(t)$ of rational functions containing the coordinate ring $B=k[t^2,t^3]$ of the cusp. An explicit example is described in detail and shown to define a quantum homogeneous space structure on the cusp, which, unlike the previously known one, extends from regular to rational functions.
