dorsal/arxiv
View SchemaOn a Deformation of $sl(2)$ with Paragrassmannian Variables
| Authors | B. Abdesselam, J. Beckers, A. Chakrabarti, N. Debergh |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507008 |
| URL | https://arxiv.org/abs/q-alg/9507008 |
| DOI | 10.1088/0305-4470/29/21/009 |
| Journal | J. Phys. A: Math. Gen. 29 (1996) 6729-6736 |
Abstract
We propose a new structure ${\cal U}^{r}_{\displaystyle{q}}(sl(2)) $. This is realized by multiplying $\delta$ ($q=e^{\delta}$, $\delta\in \CC$) by $\theta$, where $\theta$ is a real nilpotent -paragrassmannian- variable of order $r$ ($\theta^{r+1}=0$) that we call the order of deformation, the limit $r\rightarrow \infty$ giving back the standard ${\cal U}_{\displaystyle {q}}(sl(2))$. In particular we show that, for $r=1$, there exists a new ${\cal R}$-matrix associated with $sl(2)$. We also proof that the restriction of the values of the parameters of deformation give nonlinear algebras as particular cases.
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"abstract": "We propose a new structure ${\\cal U}^{r}_{\\displaystyle{q}}(sl(2)) $. This is\nrealized by multiplying $\\delta$ ($q=e^{\\delta}$, $\\delta\\in \\CC$) by $\\theta$,\nwhere $\\theta$ is a real nilpotent -paragrassmannian- variable of order $r$\n($\\theta^{r+1}=0$) that we call the order of deformation, the limit\n$r\\rightarrow \\infty$ giving back the standard ${\\cal U}_{\\displaystyle\n{q}}(sl(2))$. In particular we show that, for $r=1$, there exists a new ${\\cal\nR}$-matrix associated with $sl(2)$. We also proof that the restriction of the\nvalues of the parameters of deformation give nonlinear algebras as particular\ncases.",
"arxiv_id": "q-alg/9507008",
"authors": [
"B. Abdesselam",
"J. Beckers",
"A. Chakrabarti",
"N. Debergh"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/29/21/009",
"journal_ref": "J. Phys. A: Math. Gen. 29 (1996) 6729-6736",
"title": "On a Deformation of $sl(2)$ with Paragrassmannian Variables",
"url": "https://arxiv.org/abs/q-alg/9507008"
},
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