New W_{q,p}(sl(2)) algebras from the elliptic algebra A_{q,p}(sl(2)_c)

Jean Avan (1) , L. Frappat (2) , M. Rossi (2) , P. Sorba (2)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

We construct operators t(z) in the elliptic algebra introduced by Foda et al. A_{q,p}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 A_{q,p}(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 W_{q,p}(sl(2)) algebras.

Domaines: Algèbres quantiques [math.QA]

Jean Avan, L. Frappat, M. Rossi, P. Sorba. New W_{q,p}(sl(2)) algebras from the elliptic algebra A_{q,p}(sl(2)_c). Physics Letters A, 1998, 239, pp.27. ⟨hal-00376600⟩