For each nontrivial semisimple Hopf algebra H of dimension sixteen over \(\mathbb {C}\), the smallest dimension inner-faithful representation of H acting on a quadratic AS regular algebra A of dimension 2 or 3, homogeneously and preserving the grading, is determined. Each invariant subring A^H is determined. When A^H is also AS regular, thus providing a generalization of the Chevalley–Shephard–Todd Theorem, we say that H is a reflection Hopf algebra for A.

中文翻译：

---

十六维的半简单反射Hopf代数

对于每一个非平凡半单Hopf代数ħ尺寸16以上的\（\ mathbb {C} \） ，的最小尺寸内忠实代表ħ作用于二次AS正代数甲尺寸2或3，均匀的和保存的分级，决心，决意，决定。每一个不变的子环甲^ħ被确定。当A ^H也是AS正则，从而提供了Chevalley-Shephard-Todd定理的推广时，我们说H是A的反射Hopf代数。