Universal quantum (semi)groups and Hopf envelopes: Erratum

TL;DR

This paper discusses the correction of a previous result regarding the conditions under which the localization of the FRT construction forms a Hopf algebra, focusing on finite-dimensional Nichols algebras.

Contribution

It proposes an alternative theorem confirming that the localization of the FRT construction is a Hopf algebra when the Nichols algebra is finite dimensional.

Findings

Localization of FRT construction is a Hopf algebra for finite-dimensional Nichols algebras.

Corrects a previous computational mistake affecting main results.

Provides an affirmative answer to a key question in quantum group theory.

Abstract

In \cite{F} there is a statement generalizing the results in \cite{FG}. Unfortunately there is a mistake in a computation that affects the main result. I don't know if the main result in \cite{F} is true or not, but I propose an alternative statement (Theorem 3.7) that was actually the main motivation in \cite{FG}. This statement answers in an affirmative way the question whether the localization of the FRT construction with respect to a quantum determinant is a Hopf algebra, in case the Nichols algebra associated to the braiding is finite dimensional.