dorsal/arxiv
View SchemaUniversal $R$--matrices for non-standard (1+1) quantum groups
| Authors | A. Ballesteros, E. Celeghini, F. J. Herranz, M. A. del Olmo, M. Santander |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501030 |
| URL | https://arxiv.org/abs/q-alg/9501030 |
| DOI | 10.1088/0305-4470/28/11/015 |
| Journal | J.Phys. A28 (1995) 3129-3138 |
Abstract
A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincar\'e algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_\mu$ of ``quantum graded contractions" of the algebra $U_ziso(1,1)\oplus U_{-z}iso(1,1)$ is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional Euclidean, Poincar\'e and Galilei algebras enlarged with dilations. Universal $R$--matrices for these quantum Weyl algebras and their associated quantum groups are constructed.
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"abstract": "A universal quasitriangular $R$--matrix for the non-standard quantum (1+1)\nPoincar\\\u0027e algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the\ndeformation parameter $z$. A family $g_\\mu$ of ``quantum graded contractions\"\nof the algebra $U_ziso(1,1)\\oplus U_{-z}iso(1,1)$ is obtained; this set of\nquantum algebras contains as Hopf subalgebras with two primitive translations\nquantum analogues of the two dimensional Euclidean, Poincar\\\u0027e and Galilei\nalgebras enlarged with dilations. Universal $R$--matrices\n for these quantum Weyl algebras and their associated quantum groups are\nconstructed.",
"arxiv_id": "q-alg/9501030",
"authors": [
"A. Ballesteros",
"E. Celeghini",
"F. J. Herranz",
"M. A. del Olmo",
"M. Santander"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/28/11/015",
"journal_ref": "J.Phys. A28 (1995) 3129-3138",
"title": "Universal $R$--matrices for non-standard (1+1) quantum groups",
"url": "https://arxiv.org/abs/q-alg/9501030"
},
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