Central extensions of classical and quantum q-Viraroso algebras

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

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

We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the literature.

Domaines: Algèbres quantiques [math.QA]

Jean Avan, L. Frappat, M. Rossi, P. Sorba. Central extensions of classical and quantum q-Viraroso algebras. Physics Letters A, 1999, 251, pp.13. ⟨hal-00350839⟩