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The Sugawara construction and Casimir operators for Krichever-Novikov algebras

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References

  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).

    Article  MathSciNet  Google Scholar 

  2. R. E. Borcherds, “Vertex algebras, Kac-Moody algebras, and the monster”,Proc. Natl. Acad. Sci. USA,83, 3086–3071 (1986).

    Article  MathSciNet  Google Scholar 

  3. M. R. Bremner, “Universal central extensions of elliptic affine Lie algebras”,J. Math. Phys. 35, 6685–6692 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. R. Bremner, “Four-point affine Lie algebras,”Proc. Amer. Math. Soc.,123, 1981–1989 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  5. I. Frenkel, J. Lepowski, and A. Meurman,Vertex Operator Algebras and the Monster, Academic Press, Boston (1988).

    MATH  Google Scholar 

  6. A. Jaffe, S. Klimek, and A. Lesniewski, “Representations of the Heisenberg algebra, on a Riemann surface,”Commun. Math. Phys.,126, 421–431 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. Kac,Infinite-dimensional Lie Algebras, Cambridge University Press, Cambridge (1990).

    MATH  Google Scholar 

  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).

  9. I. M. Krichever,Personal communication (1995).

  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).

    MATH  MathSciNet  Google Scholar 

  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).

    Article  MATH  MathSciNet  Google Scholar 

  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.

  13. V. A. Sadov, “Bases on multipunctured Riemann surfaces and interacting string amplitudes,”Commun. Math. Phys.,136, 585–597 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Schlichenmaier,An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces [Springer Lecture Notes in Physics, Vol. 322] Springer, New York (1989).

    MATH  Google Scholar 

  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).

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Schlichenmaier, “Verallgemeinerte Krichever-Novikov Algebren und deren Darstellungen,”PhD. Thesis, Universität Mannheim, Germany (1990).

    MATH  Google Scholar 

  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. 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).

    Article  MATH  MathSciNet  Google Scholar 

  19. O. K. Sheinman, “Highest-weight modules for affine Lie algebras on Riemann surfaces,”Funkts. Anal. Prilozhen.,28, No. 1 (1995).

    Google Scholar 

  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 

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Authors
  1. M. Schlichenmaier
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  2. O. K. Scheinman
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Maternatika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 38. Complex Analysis and Representation Theory-1. 1996.

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Schlichenmaier, M., Scheinman, O.K. The Sugawara construction and Casimir operators for Krichever-Novikov algebras. J Math Sci 92, 3807–3834 (1998). https://doi.org/10.1007/BF02434007

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