We describe how to find quantum determinants and antipode formulas from braided vector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improves the construction of quantum function algebras using quantum grassmanian algebras. Given a finite-dimensional Nichols algebra $\mathfrak B$, our method provides a Hopf algebra $H$ such that $\mathfrak B$ is a braided Hopf algebra in the category of $H$-comodules. It also serves as source to produce Hopf algebras generated by cosemisimple subcoalgebras, which are of interest for the generalized lifting method. We give several examples, among them quantum function algebras from Fomin–Kirillov algebras associated with the symmetric group on three letters.

中文翻译：

---

有限维尼科尔斯代数的量子函数代数

我们描述了如何使用FRT构造和有限维Nichols代数从编织向量空间中找到量子行列式和对映式。它使用量子格拉斯曼代数改进了量子函数代数的构造。给定有限维的Nichols代数$ \ mathfrak B $，我们的方法提供了Hopf代数$ H $，使得$ \ mathfrak B $是$ H $ -comodules类别中的编织Hopf代数。它也可以用作产生由准半简单次代数生成的Hopf代数的源，这对于广义提升方法很有用。我们给出几个例子，其中包括与三个字母上的对称基团相关的Fomin–Kirillov代数的量子函数代数。