Journal of Mathematical Sciences

, Volume 92, Issue 2, pp 3807–3834 | Cite as

The Sugawara construction and Casimir operators for Krichever-Novikov algebras

  • M. Schlichenmaier
  • O. K. Scheinman


Riemann Surface Central Extension Quadratic Differential Casimir Operator Admissible Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Bonora L. M. Rinaldi, J. Russo, and K. Wu, “The Sugawara construction on genusg Riemann surfaces”,Phys. Lett. B,208, 440–446 (1988).MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. E. Borcherds, “Vertex algebras, Kac-Moody algebras, and the monster”,Proc. Natl. Acad. Sci. USA,83, 3086–3071 (1986).MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. R. Bremner, “Universal central extensions of elliptic affine Lie algebras”,J. Math. Phys. 35, 6685–6692 (1994).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. R. Bremner, “Four-point affine Lie algebras,”Proc. Amer. Math. Soc.,123, 1981–1989 (1995).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    I. Frenkel, J. Lepowski, and A. Meurman,Vertex Operator Algebras and the Monster, Academic Press, Boston (1988).zbMATHGoogle Scholar
  6. 6.
    A. Jaffe, S. Klimek, and A. Lesniewski, “Representations of the Heisenberg algebra, on a Riemann surface,”Commun. Math. Phys.,126, 421–431 (1989).zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    V. Kac,Infinite-dimensional Lie Algebras, Cambridge University Press, Cambridge (1990).zbMATHGoogle Scholar
  8. 8.
    V. G. Kac and A. K. Raina,Highest-Weight Representations of Infinite-Dimensional Lie Algebras [Adv. Ser. in Math. Physics Vol. 2], World Scientific (1987).Google Scholar
  9. 9.
    I. M. Krichever,Personal communication (1995).Google Scholar
  10. 10.
    I. M. Krichever and S. P. Novikov, “Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons,”Funkts. Anal. Prilozhen,21, No. 2, 46 (1987); “Virasoro type algebras, Riemann surfaces and strings in Minkowski space,”Funkts. Anal. Prilozhen.,21, No. 4, 47 (1987); “Algebras of Virasoro type, energy-momentum tensors and decompositions of operators on Riemann surfaces,”Funkts. Anal. Prilozhen.,23, No. 1, 19–23 (1989).zbMATHMathSciNetGoogle Scholar
  11. 11.
    I. M. Krichever and S. P. Novikov, “Virasoro-Gelfand-Fuks type algebras, Riemann surfaces operator's theory of closed strings,”JGP,5, 631–661 (1988).zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    I. M. Krichever and S. P. Novikov, “Riemannn surfaces. Operator fields, Strings. Analogues of Fourier-Laurent bases,” In:Physics and Mathematics of Strings (Brink, Friedan, Polyakov, eds.), World Scientific (1990), pp. 356–388.Google Scholar
  13. 13.
    V. A. Sadov, “Bases on multipunctured Riemann surfaces and interacting string amplitudes,”Commun. Math. Phys.,136, 585–597 (1991).zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    M. Schlichenmaier,An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces [Springer Lecture Notes in Physics, Vol. 322] Springer, New York (1989).zbMATHGoogle Scholar
  15. 15.
    M. Schlichenmaier, “Krichever-Novikov algebras for more than two points,”Lett. Math., Phys.,19, 151–165 (1990); “Krichever-Novikov algebras for more than two points: explicit generators,”Lett. Math. Phys.,19, 327–336 (1990); “Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points,”Lett. Math. Phys.,20, 33–46 (1990).zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    M. Schlichenmaier, “Verallgemeinerte Krichever-Novikov Algebren und deren Darstellungen,”PhD. Thesis, Universität Mannheim, Germany (1990).zbMATHGoogle Scholar
  17. 17.
    M. Schlichenmaier, “Differential operator algebras on compact Riemann surfaces” In:Generalized Sympmetries in Physics. (H.-D. Doebner, V. K. Dobrev, and A. G. Ushveridze, eds.), World Scientific, Singapore-London (1994), pp., 425–435.Google Scholar
  18. 18.
    O. K. Sheinman, “Elliptic affine Lie algebras,”Funkts. Anal. Prilozhen.,24, No. 3, 210–219 (1990): “Highest-weight modules over certain quasigraded Lie algebras on elliptic curves,”Funkts. Anal. Prilozhen,26. No. 3, 203–208 (1992); “Affine Lie algebras on Riemann surfaces,”Funkts. Anal. Prilozhen.,27. No. 4, 54–62 (1993).zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    O. K. Sheinman, “Highest-weight modules for affine Lie algebras on Riemann surfaces,”Funkts. Anal. Prilozhen.,28, No. 1 (1995).Google Scholar
  20. 20.
    O. K. Sheinman, “Representations of Krichever-Novikov algebras,” In:Topics in Topology and Mathematical Physics (S. P. Novikov, ed.), Amer. Math. Soc., Providence, Rhode Island (1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • M. Schlichenmaier
  • O. K. Scheinman

There are no affiliations available

Personalised recommendations