We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra . We discuss two cases, according to whether the parameter is a root of unity. We show that the universal enveloping algebra of embeds in a non-principal ultraproduct of , where varies over the primitive roots of unity.
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Mots-clés : Quantum algebra, quantum plane, exponential map, ultraproduct
@article{CML_2013__5_2_49_0,
author = {L{\textquoteright}Innocente, Sonia and Point, Fran\c{c}oise and Toffalori, Carlo},
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 = {http://www.numdam.org/articles/10.5802/cml.8/}
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PY - 2013
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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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