Letters in Mathematical Physics

, Volume 31, Issue 1, pp 65–76 | Cite as

The Lie algebra of the sl(2, ℂ)-valued automorphic functions on a torus

  • D. B. Uglov


It is shown that the Lie algebra of the automorphic, meromorphic sl(2, ℂ)-valued functions on a torus is a geometric realization of a certain infinite-dimensional finitely generated Lie algebra. In the trigonometric limit, when the modular parameter of the torus goes to zero, the former Lie algebra goes over into the sl(2, ℂ)-valued loop algebra, while the latter goes into the Lie algebra (A 1 (1) )′/(centre).

Mathematics Subject Classification (1991)



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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • D. B. Uglov
    • 1
  1. 1.Department of PhysicsState University of New York at Stony BrookStony BrookUSA

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