Quantum function algebras from finite-dimensional Nichols algebras

Abstract

We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using quantum grassmanian algebras.Given a finite-dimensional Nichols algebra B, our method provides a Hopf algebraH such that B is a braided Hopf algebra in the category of H-comodules. It also serves assource to produce Hopf algebras generated by cosemisimple subcoalgebras, which are ofinterest for the generalized lifting method. We give several examples, among them quantumfunction algebras from Fomin-Kirillov algebras associated with the symmetric groupon three letters.