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

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

1997-06-13

arxiv.org/abs/q-alg/9706013v1

Phys.Lett. A239 (1998) 27-35

Mathematics

Quantum Algebra

9 pages; Warning: LaTeX2e Document - packages subeqn,amsfonts

Scientific paper

10.1016/S0375-9601(97)00940-7

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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