Poisson structures on the center of the elliptic algebra A_{p,q}(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

It is shown that the elliptic algebra A_{p,q}(sl(2)_c) has a non trivial center at the critical level c=-2, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric algebras. A family of Poisson structures indexed by a non-negative integer k is constructed on this center.

Domaines: Algèbres quantiques [math.QA]; Physique des Hautes Energies - Théorie [hep-th]

Jean Avan, L. Frappat, M. Rossi, P. Sorba. Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c). Physics Letters A, 1997, 235, pp.323. ⟨hal-00376599⟩