dorsal/arxiv
View SchemaNew ${\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\cal A}_{q,p}({\hat sl}(2)_c)$
| Authors | J. Avan, L. Frappat, M. Rossi, P. Sorba |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706013 |
| URL | https://arxiv.org/abs/q-alg/9706013 |
| DOI | 10.1016/S0375-9601(97)00940-7 |
| Journal | Phys.Lett. A239 (1998) 27-35 |
Abstract
We construct operators t(z) in the elliptic algebra introduced by Foda et al. ${\cal A}_{q,p}({\hat sl}(2)_c)$. They close an exchange algebra when p^m=q^{c+2} for m integer. In addition they commute when p=q^{2k} for k integer non-zero, and they belong to the center of ${\cal A}_{q,p}({\hat sl}(2)_c)$ when k is odd. The Poisson structures obtained for t(z) in these classical limits are identical to the q-deformed Virasoro Poisson algebra, characterizing the exchange algebras at generic values of p, q and m as new ${\cal W}_{q,p}(sl(2))$ algebras.
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"abstract": "We construct operators t(z) in the elliptic algebra introduced by Foda et al.\n${\\cal A}_{q,p}({\\hat sl}(2)_c)$. They close an exchange algebra when\np^m=q^{c+2} for m integer. In addition they commute when p=q^{2k} for k integer\nnon-zero, and they belong to the center of ${\\cal A}_{q,p}({\\hat sl}(2)_c)$\nwhen k is odd. The Poisson structures obtained for t(z) in these classical\nlimits are identical to the q-deformed Virasoro Poisson algebra, characterizing\nthe exchange algebras at generic values of p, q and m as new ${\\cal\nW}_{q,p}(sl(2))$ algebras.",
"arxiv_id": "q-alg/9706013",
"authors": [
"J. Avan",
"L. Frappat",
"M. Rossi",
"P. Sorba"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1016/S0375-9601(97)00940-7",
"journal_ref": "Phys.Lett. A239 (1998) 27-35",
"title": "New ${\\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\\cal A}_{q,p}({\\hat sl}(2)_c)$",
"url": "https://arxiv.org/abs/q-alg/9706013"
},
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