Deformed Algebras from Elliptic sl(N) Algebras

Abstract:

We extend to the case the results that we previously obtained on the construction of algebras from the elliptic algebra . The elliptic algebra at the critical 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 algebra, are constructed. The operators t(z) also close an exchange algebra when for . It becomes Abelian when in addition p=q ^Nh, where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed algebras depending on the parity of h, characterizing the exchange structures at p≠q ^Nh as new algebras.