dorsal/arxiv
View SchemaCombined (q,h)-Deformation as a Nonlinear Map on $U_q(sl(2))$
| Authors | B. Abdesselam, A. Chakrabarti, R. Chakrabarti |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612028 |
| URL | https://arxiv.org/abs/q-alg/9612028 |
Abstract
The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet $({\hat X},{\hat Y},{\hat H})$. The latter set forms a closed algebra under commutation relations. The nonlinear algebra $U_{q,h}(sl(2))$, thus generated, has two different limits. For $q \to 1$, the Jordanian h-deformation $U_{h}(sl(2))$ is obtained. For $h \to 0$, the q-deformed algebra $U_{q}(sl(2))$ is reproduced. From the nonlinear map, the irreducible representations of the doubly-deformed algebra $U_{q,h}(sl(2))$ may be directly and explicitly obtained form the known representations of the algebra $U_q(sl(2))$. Here we consider only generic values of q.
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"abstract": "The generators $(J_{\\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting\npoint. An invertible nonlinear map involving, apart from q, a second arbitrary\ncomplex parameter h, defines a triplet $({\\hat X},{\\hat Y},{\\hat H})$. The\nlatter set forms a closed algebra under commutation relations. The nonlinear\nalgebra $U_{q,h}(sl(2))$, thus generated, has two different limits. For $q \\to\n1$, the Jordanian h-deformation $U_{h}(sl(2))$ is obtained. For $h \\to 0$, the\nq-deformed algebra $U_{q}(sl(2))$ is reproduced. From the nonlinear map, the\nirreducible representations of the doubly-deformed algebra $U_{q,h}(sl(2))$ may\nbe directly and explicitly obtained form the known representations of the\nalgebra $U_q(sl(2))$. Here we consider only generic values of q.",
"arxiv_id": "q-alg/9612028",
"authors": [
"B. Abdesselam",
"A. Chakrabarti",
"R. Chakrabarti"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Combined (q,h)-Deformation as a Nonlinear Map on $U_q(sl(2))$",
"url": "https://arxiv.org/abs/q-alg/9612028"
},
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