Central extensions of classical and quantum q-Virasoro algebras

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. (C) 1999 Published by Elsevier Science B.V.