# CONFLUENTES MATHEMATICI

Exponentiations over the quantum algebra ${U}_{q}\left(s{l}_{2}\left(ℂ\right)\right)$
Confluentes Mathematici, Tome 5 (2013) no. 2, pp. 49-77.

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra ${U}_{q}\left(s{l}_{2}\left(ℂ\right)\right)$. We discuss two cases, according to whether the parameter $q$ is a root of unity. We show that the universal enveloping algebra of $s{l}_{2}\left(ℂ\right)$ embeds in a non-principal ultraproduct of ${U}_{q}\left(s{l}_{2}\left(ℂ\right)\right)$, where $q$ varies over the primitive roots of unity.

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DOI : https://doi.org/10.5802/cml.8
Classification : 03C60,  16W35,  20G42,  81R50
Mots clés : Quantum algebra, quantum plane, exponential map, ultraproduct
@article{CML_2013__5_2_49_0,
author = {Sonia L{\textquoteright}Innocente and Fran\c{c}oise Point and Carlo Toffalori},
title = {Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$},
journal = {Confluentes Mathematici},
pages = {49--77},
publisher = {Institut Camille Jordan},
volume = {5},
number = {2},
year = {2013},
doi = {10.5802/cml.8},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.8/}
}
Sonia L’Innocente; Françoise Point; Carlo Toffalori. Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$. Confluentes Mathematici, Tome 5 (2013) no. 2, pp. 49-77. doi : 10.5802/cml.8. https://cml.centre-mersenne.org/articles/10.5802/cml.8/

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