dorsal/arxiv
View SchemaFrom quantum to elliptic algebras
| Authors | J. Avan, L. Frappat, M. Rossi, P. Sorba |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707034 |
| URL | https://arxiv.org/abs/q-alg/9707034 |
| DOI | 10.1023/A:1021645814342 |
Abstract
It is shown that the elliptic algebra ${\cal A}_{q,p}(\hat{sl}(2)_c)$ at the critical level c=-2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m integer, they commute when in addition 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 contain the q-deformed Virasoro algebra, characterizing the structures at generic values of p, q and m as new ${\cal W}_{q,p}(sl(2))$ algebras.
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"abstract": "It is shown that the elliptic algebra ${\\cal A}_{q,p}(\\hat{sl}(2)_c)$ at the\ncritical level c=-2 has a multidimensional center containing some trace-like\noperators t(z). A family of Poisson structures indexed by a non-negative\ninteger and containing the q-deformed Virasoro algebra is constructed on this\ncenter. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m\ninteger, they commute when in addition p=q^{2k} for k integer non-zero, and\nthey belong to the center of ${\\cal A}_{q,p}(\\hat{sl}(2)_c)$ when k is odd. The\nPoisson structures obtained for t(z) in these classical limits contain the\nq-deformed Virasoro algebra, characterizing the structures at generic values of\np, q and m as new ${\\cal W}_{q,p}(sl(2))$ algebras.",
"arxiv_id": "q-alg/9707034",
"authors": [
"J. Avan",
"L. Frappat",
"M. Rossi",
"P. Sorba"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1023/A:1021645814342",
"title": "From quantum to elliptic algebras",
"url": "https://arxiv.org/abs/q-alg/9707034"
},
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