Universal quantum (semi)groups and Hopf envelopes: Erratum
Marco Farinati

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
