New ${\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\cal A}_{q,p}({\hat sl}(2)_c)$

J. Avan; L. Frappat; M. Rossi; P. Sorba

doi:10.1016/s0375-9601(97)00940-7

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arXiv · q-alg/9706013

New ${\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\cal A}_{q,p}({\hat sl}(2)_c)$

J. Avan·L. Frappat·M. Rossi·P. Sorba

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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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BibTeX RIS

J. Avan, L. Frappat, M. Rossi, P. Sorba. 1997-06-13. New ${\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\cal A}_{q,p}({\hat sl}(2)_c)$. https://doi.org/10.1016/s0375-9601(97)00940-7

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