Exponentiations over the quantum algebra U q (sl 2 ())
Confluentes Mathematici, Tome 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.

Reçu le : 2012-06-17
Révisé le : 2013-06-23
Accepté le : 2013-06-23
Publié le : 2017-03-26
DOI : https://doi.org/10.5802/cml.8
Classification : 03C60,  16W35,  20G42,  81R50
Mots clés: Quantum algebra, quantum plane, exponential map, ultraproduct
     author = {Sonia L'Innocente and Fran\c coise Point and Carlo Toffalori},
     title = {Exponentiations over the quantum algebra $U\_{q}(sl\_2(\mathbb{C}))$},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {5},
     number = {2},
     year = {2013},
     pages = {49-77},
     doi = {10.5802/cml.8},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2013__5_2_49_0/}
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/item/CML_2013__5_2_49_0/

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