# CONFLUENTES MATHEMATICI

Exponentiations over the quantum algebra ${U}_{q}\left(s{l}_{2}\left(ℂ\right)\right)$
Confluentes Mathematici, Volume 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.

Revised:
Accepted:
Published online:
DOI: 10.5802/cml.8
Classification: 03C60,  16W35,  20G42,  81R50
Keywords: Quantum algebra, quantum plane, exponential map, ultraproduct
Sonia L’Innocente 1; Françoise Point 2; Carlo Toffalori 3

1 School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC), Italy
2 Institut de mathématique, Le Pentagone, Université de Mons, 20, place du Parc, B-7000 Mons, Belgium.
3 School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC) Italy
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Sonia L’Innocente; Françoise Point; Carlo Toffalori. Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$. Confluentes Mathematici, Volume 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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