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Exponentiations over the quantum algebra $U_{q} (s l_{2} (ℂ))$

Sonia L’Innocente; Françoise Point; Carlo Toffalori — 2013

Confluentes Mathematici

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

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