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Sonia L’Innocente; Françoise Point; Carlo Toffalori
Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$
Confluentes Mathematici, 5 no. 2 (2013), p. 49-77
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Class. Math.: 03C60, 16W35, 20G42, 81R50
Mots clés: Quantum algebra, quantum plane, exponential map, ultraproduct

Résumé - Abstract

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra $U_q(sl_2(\mathbb{C}))$. We discuss two cases, according to whether the parameter $q$ is a root of unity. We show that the universal enveloping algebra of $sl_{2}(\mathbb{C})$ embeds in a non-principal ultraproduct of $U_q(sl_2(\mathbb{C}))$, where $q$ varies over the primitive roots of unity.

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