Skip to main content
SpringerLink
Log in

A sketch of Lie superalgebra theory

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

This article deals with the structure and representations of Lie superalgebras (ℤ2-graded Lie algebras). The central result is a classification of simple Lie superalgebras over ℝ and ℂ.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andreev, E. M., Vinberg, E. B., Elashvili, A. G.: Funct. Anal.1, n. 4, 3–7 (1967) (Russian)

    Google Scholar 

  2. Berezin, F. A.: The method of second quantization. New York: Academic Press 1966

    Google Scholar 

  3. Berezin, F. A.: Math. zametki1, 269–276 (1967) (Russian)

    Google Scholar 

  4. Berezin, F. A., Kac, G. I.: Math. Sbornik82, 343–351 (1970) (Russian)

    Google Scholar 

  5. Berezin, F. A., Leites, D. A.: Dokl. Akad. Nauk SSSR224, 505–509, (1975) (Russian)

    Google Scholar 

  6. Weisfeiler, B. Ju.: Funct. Anal.2, n. 1, 94–95 (1968) (Russian)

    Google Scholar 

  7. Weisfeiler, B. Ju., Kac, V. G.: Funct. Anal.5, n. 2, 28–36 (1971) (Russian)

    Google Scholar 

  8. Weisfeiler, B. Ju., Kac, V. G.: Izv. Acad. Nauk. Ser Math.35, 762–788 (1971) (Russian)

    Google Scholar 

  9. Vinberg, E. B., Onistchik, A. L.: Seminar on algebraic groups and Lie groups. Moscow University 1969 (Russian)

  10. Jacobson, N.: Lie algebras. Intersc. Tracts10, (1962)

  11. Kac, V. G.: Izv. Acad. Nauk. Ser. Math.32, 1323–1367 (1968) (Russian)

    Google Scholar 

  12. Kac, V. G.: Izv. Acad. Nauk. Ser. Math.34, 385–408 (1970) (Russian)

    Google Scholar 

  13. Kac, V. G.: All-Union algebraic colloquium, Kishinev, ⋆⋆ 140–141 (1971) (Russian)

  14. Kac, V. G.: Funct. Anal.8, n. 1, 77–78 (1974) (Russian)

    Google Scholar 

  15. Kac, V. G.: Izv. Acad. Nauk. Ser. Math.38, 800–834 (1974) (Russian)

    Google Scholar 

  16. Kac, V. G.: Funct. Anal.9, n. 3, 91–92 (1975) (Russian)

    Google Scholar 

  17. Leites, D. A.: Funct. Anal.9, n. 4, 75–76 (1975) (Russian)

    Google Scholar 

  18. Rudakov, A. N.: Izv. Acad. Nauk. Ser. Math.33, 748–764, 1969 (Russian)

    Google Scholar 

  19. Stavraky, G. L.: High energies physics and theory of elementary particles, Kiev: ⋆⋆, 297–312 (1966) (Russian)

  20. Blattner, R. J.: Trans. Amer. Math. Soc.144, 457–474 (1969)

    Google Scholar 

  21. Block, R. E.: Ann. Math.90, 433–459 (1969)

    Google Scholar 

  22. Corwin, L., Ne'eman, Y., Sternberg, S.: Rev. Mod. Phys.47, 573–603 (1975)

    Google Scholar 

  23. Kobayashi, S., Nagano, T.: J. Math. Mech.14, 679–706, (1965)

    Google Scholar 

  24. Kac, V. G.: Funct. Anal.10, n. 2, 93 (1976) (Russian)

    Google Scholar 

  25. Ogievetsky, V. I., Mezincescu, L.: Uspehi Fizich. Nauk.117, 637–683 (1975) (Russian)

    Google Scholar 

  26. Pais, A., Rittenberg, V.: J. Math. Phys.16, 2062 (1975)

    Google Scholar 

  27. Kaplansky, I.: preprint

  28. Freund, P. G. O., Kaplansky, I.: J. Math. Phys.17, 228 (1976)

    Google Scholar 

  29. Djoković, D. Z.: preprint

  30. Scheunert, M., Nahm, W., Rittenberg, V.: preprint

  31. Kac, V. G.: preprint

Download references

Author information

Authors and Affiliations

  1. Moscow Institute for Electronics Equipment, Moscow, USSR

    V. G. Kac

Authors
  1. V. G. Kac
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. Haag

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kac, V.G. A sketch of Lie superalgebra theory. Commun.Math. Phys. 53, 31–64 (1977). https://doi.org/10.1007/BF01609166

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01609166

Keywords

Search

Navigation