Deformed \(\) Algebras from Elliptic sl(N) Algebras
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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.
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