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.
@article{CML_2013__5_2_49_0,
author = {Sonia L{\textquoteright}Innocente and Fran\c{c}oise Point and Carlo Toffalori},
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 = {https://cml.centre-mersenne.org/articles/10.5802/cml.8/}
}
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AU - Sonia L’Innocente
AU - Françoise Point
AU - Carlo Toffalori
TI - Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$
JO - Confluentes Mathematici
PY - 2013
SP - 49
EP - 77
VL - 5
IS - 2
PB - Institut Camille Jordan
UR - https://cml.centre-mersenne.org/articles/10.5802/cml.8/
DO - 10.5802/cml.8
LA - en
ID - CML_2013__5_2_49_0
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Sonia L’Innocente; Françoise Point; Carlo Toffalori. Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$. Confluentes Mathematici, Tome 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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