Exponentiations over the quantum algebra U q (sl 2 ())
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 (sl 2 ()). We discuss two cases, according to whether the parameter q is a root of unity. We show that the universal enveloping algebra of sl 2 () embeds in a non-principal ultraproduct of U q (sl 2 ()), where q varies over the primitive roots of unity.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/cml.8
Classification: 03C60, 16W35, 20G42, 81R50
Mots-clés : Quantum algebra, quantum plane, exponential map, ultraproduct
L’Innocente, Sonia 1; Point, Françoise 2; Toffalori, Carlo 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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L’Innocente, Sonia; Point, Françoise; Toffalori, Carlo. 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. http://www.numdam.org/articles/10.5802/cml.8/

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