Communications in Mathematical Physics

, Volume 178, Issue 3, pp 653–677 | Cite as

Quantum Open image in new window -algebras and elliptic algebras

  • Boris Feigin
  • Edward Frenkel


We define a quantum
-algebra associated to\(\mathfrak{s}\mathfrak{l}_N \) as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary
-algebra of\(\mathfrak{s}\mathfrak{l}_N \), or theq-deformed classical
-algebra algebra of\(\mathfrak{s}\mathfrak{l}_N \). We construct free field realizations of the quantum
-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Boris Feigin
    • 1
    • 2
  • Edward Frenkel
    • 3
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.R.I.M.S.Kyoto UniversityKyotoJapan
  3. 3.Department of MathematicsHarvard UniversityCambridgeUSA

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