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Communications in Mathematical Physics

, Volume 199, Issue 3, pp 697–728 | Cite as

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

  • J. Avan
  • L. Frappat
  • M. Rossi
  • P. Sorba

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 pq Nh as new \(\) algebras.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • J. Avan
    • 1
  • L. Frappat
    • 2
  • M. Rossi
    • 2
  • P. Sorba
    • 2
  1. 1.LPTHE, CNRS-URA 280, Universités Paris VI/VII, FranceFR
  2. 2.Laboratoire de Physique Théorique LAPTH, URA 1436, CNRS and Université de Savoie, FranceFR

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