Quantum function algebras from finite-dimensional Nichols algebras
Abstract
We describe how to find quantum determinants and antipode formulas from braided vector spaces using the FRT-construction and finite-dimensional Nichols algebras. It generalizes the construction of quantum function algebras using quantum grassmanian algebras. Given a finite-dimensional Nichols algebra B, our method provides a Hopf algebra H such that 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 groups on three letters.
Keywords
Cite
@article{arxiv.1805.11736,
title = {Quantum function algebras from finite-dimensional Nichols algebras},
author = {Marco A. Farinati and Gaston Andres Garcia},
journal= {arXiv preprint arXiv:1805.11736},
year = {2021}
}
Comments
25 pages. Some remarks added after referee's suggestion, particularly, on the existence of localization (with or without Ore condition) and on the type of examples. Some references added