# Universal Quantum (Semi)groups and Hopf Envelopes

@article{Farinati2022UniversalQ, title={Universal Quantum (Semi)groups and Hopf Envelopes}, author={Marco A. Farinati}, journal={Algebras and Representation Theory}, year={2022} }

We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite dimensional), then the Hopf envelope of $A(c)$ is simply the localization of $A(c)$ by a single element called the quantum determinant associated to the weakly Frobenius algebra. This generalizes a result of the author together with Gast\'on A. Garc\'ia in \cite{FG}, where the same statement was…

## 2 Citations

Universal quantum (semi)groups and Hopf envelopes: Erratum

- Mathematics
- 2022

In [F] there is a statement generalizing the results in [FG]. Unfortunately there is a mistake in a computation that affects the main result. I don’t know if the main result in [F] is true or not,…

Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation

- Mathematics
- 2021

Let H be a Hopf algebra that is Z-graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of H to be a Zhang twist of H. In particular, we introduce the notion of a twisting pair…

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