Skip to main content

A guide to Lie superalgebras

  • Invited Lectures
  • Conference paper
  • First Online:
Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 79))

Abstract

We give an elementary presentation of the Lie superalgebras, their classification and some properties of their representations. A sketch of the classical Lie supergroup is also given.

Invited talk at the VI International Colloquium on Group Theoretical Methods in Physics, Tübingen, July 18–22, 1977.

On leave from the Physikalisches Institut Bonn.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Irving Kaplansky, Lie and Jordan superalgebras, Chicago report 1977.

    Google Scholar 

  2. L. Corwin, Y. Ne'eman and S. Sternberg, Rev. Mod. Phys. 47, 573 (1975).

    Google Scholar 

  3. V.G. Kac, Communications in Mathematical Phys. 53, 31 (1977).

    Google Scholar 

  4. P. Fayet and S. Ferrara, Physics Reports, to be published.

    Google Scholar 

  5. S. Ferara, in these proceedings.

    Google Scholar 

  6. A. Pais and V. Rittenberg, J. Math. Phys., 16, 2062 (1975), 17, 598 (1976).

    Google Scholar 

  7. P.G.O. Freund and I. Kaplansky, J. Math. Phys. 17, 228 (1976); I.Kaplansky, Univ. of Chicago preprint (1976).

    Google Scholar 

  8. W. Nahm and M. Scheunert, J. Math. Phys. 17, 868 (1976).

    Google Scholar 

  9. N.B. Backhouse, J. Math. Phys. 18, 339 (1977).

    Google Scholar 

  10. V.G. Kac, to be published.

    Google Scholar 

  11. See for example L. Michel in Group representations in Mathematics and Physics, p.136; Springer; Berlin, Heidelberg (1970).

    Google Scholar 

  12. A. Pais, J. Math. Phys. 3, 1135 (1962).

    Google Scholar 

  13. Bernice Durand, Institute for Advanced Study, Princeton preprint (1976).

    Google Scholar 

  14. W. Nahm, V. Rittenberg and M. Scheunert, Phys. Lett. B61, 383 (1976).

    Google Scholar 

  15. M. Scheunert, W. Nahm and V. Rittenberg, J. Math.Phys. 17, 1626, 1640 (1976).

    Google Scholar 

  16. V.G. Kac, Functional Analysis and Applications, 9, 91 (1975) (Russian).

    Google Scholar 

  17. G. Hochschild, Ill. J. Math.20, 107 (1976). D.Z. Djokovic and G. Hochschild, Ill. J. Math. 20,134(1976);D.Z.Djokovic,J.Pure.Appl.Alg.7,217 (1976).

    Google Scholar 

  18. M. Scheunert, W. Nahm and V. Rittenberg, J. Math. Phys. 18, 155 (1977).

    Google Scholar 

  19. M. Scheunert, W. Nahm and V. Rittenberg, J. Math. Phys. 18, 146 (1977).

    Google Scholar 

  20. G.L. Stavraki, in high energy physics and the theory of elementary particles, Nankova Dumka, Kiev, 1966.

    Google Scholar 

  21. V.G. Kac, Some remarks on Lie superalgebras theory (MIT report 1977).

    Google Scholar 

  22. B. Kostant, Graded manifolds, graded Lie theory and prequantization, MIT report.

    Google Scholar 

  23. F.A. Berezin, Funkc. analiz. 10, 70 (1976) and references therein.

    Google Scholar 

  24. V. Rittenberg, M. Scheunert, Bonn-HE-77-13 (1977) preprint.

    Google Scholar 

  25. Feza Gursey, Louis Marchildon, Yale preprint 1977.

    Google Scholar 

  26. D.A. Leites, Uspechi. Mat. nauk. 30, 156 (1975).

    Google Scholar 

  27. V.G. Kac, Characters of typical representations of classical Lie algebras MIT report 1977.

    Google Scholar 

  28. V.F. Pakhomov, Math. Notes. Acad. Sciences USSR 16, 624 (1974).

    Google Scholar 

  29. I.I. Bernstein and D.A. Leites, Functional Analysis and Applications 11, 55 (1977) (Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

P. Kramer A. Rieckers

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Rittenberg, V. (1978). A guide to Lie superalgebras. In: Kramer, P., Rieckers, A. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08848-2_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-08848-2_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08848-6

  • Online ISBN: 978-3-540-35813-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics