Exponentiations over the quantum algebra U q ( s l 2 ( ℂ ) )

Sonia L’Innocente[1]; Françoise Point[2]; Carlo Toffalori[3]

  • [1] School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC), Italy
  • [2] Institut de mathématique, Le Pentagone, Université de Mons, 20, place du Parc, B-7000 Mons, Belgium.
  • [3] School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC) Italy

Confluentes Mathematici (2013)

  • Volume: 5, Issue: 2, page 45-69
  • ISSN: 1793-7434

Abstract

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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.

How to cite

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L’Innocente, Sonia, Point, Françoise, and Toffalori, Carlo. "Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$." Confluentes Mathematici 5.2 (2013): 45-69. <http://eudml.org/doc/275651>.

@article{L2013,
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.},
affiliation = {School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC), Italy; Institut de mathématique, Le Pentagone, Université de Mons, 20, place du Parc, B-7000 Mons, Belgium.; School of Science and Technology, Division of Mathematics, University of Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC) Italy},
author = {L’Innocente, Sonia, Point, Françoise, Toffalori, Carlo},
journal = {Confluentes Mathematici},
keywords = {Quantum algebra; quantum plane; exponential map; ultraproduct; quantum algebra; universal enveloping algebra},
language = {eng},
number = {2},
pages = {45-69},
publisher = {Institut Camille Jordan},
title = {Exponentiations over the quantum algebra $U_\{q\}(sl_2(\mathbb\{C\}))$},
url = {http://eudml.org/doc/275651},
volume = {5},
year = {2013},
}

TY - JOUR
AU - L’Innocente, Sonia
AU - Point, Françoise
AU - Toffalori, Carlo
TI - Exponentiations over the quantum algebra $U_{q}(sl_2(\mathbb{C}))$
JO - Confluentes Mathematici
PY - 2013
PB - Institut Camille Jordan
VL - 5
IS - 2
SP - 45
EP - 69
AB - 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.
LA - eng
KW - Quantum algebra; quantum plane; exponential map; ultraproduct; quantum algebra; universal enveloping algebra
UR - http://eudml.org/doc/275651
ER -

References

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  10. A. Macintyre. Model theory of exponentials on Lie algebras. Math. Structures Comput. Sci. 18:189–204, 2008. Zbl1138.03030MR2459619
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