Deformed W-N algebras from elliptic sl(N) algebras

We extend to the sl(N) case the results that we previously obtained on the construction of W-q,W-p algebras from the elliptic algebra A(q,p)(<(sl)over cap>(2)(c)). The elliptic algebra A(q,p)(<(sl)over cap>(N)(c)) at the crit ical level c = -N has an extended center containing trace-like operators t( z). Families of Poisson structures indexed by N(N - 1)/2 integers, defining q-deformations of the W-N algebra, are constructed. The operators t(z) als o close an exchange algebra when (-p(1/2))(NM) = q(-c-N) for M is an elemen t of Z. It becomes Abelian when in addition p = q(Nh), where h is a non-zer o integer, The Poisson structures obtained in these classical limits contai n different q-deformed W-N algebras depending on the parity of h, character izing the exchange structures at p not equal q(Nh) as new W-q,W-p(sl(N)) al gebras.