Skip to main content
SpringerLink
Log in

A “new” proof of kaplansky's theorem on simple Lie algebras of rank one

  • Lie Algebras
  • Conference paper
  • First Online:
Algebra Carbondale 1980

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 848))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. K. Amayo, "Quasi-ideals of Lie algebras I", Proc. London Math. Soc. (3) 33 (1976), 28–36.

    Article  MathSciNet  MATH  Google Scholar 

  2. _____, "Quasi-ideals of Lie algebras II", Proc. London Math. Soc. (3) 33 (1976), 37–64.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. M. Benkart, I. M. Isaacs, and J. M. Osborn, "Lie algebras with self-centralizing ad-nilpotent elements", J. Algebra 57 (1979), 279–309.

    Article  MathSciNet  MATH  Google Scholar 

  4. G.M. Benkart and I.M. Isaacs, "Lie algebras with nilpotent centralizers", Canad. J. Math. 31 (1979), 929–941.

    Article  MathSciNet  MATH  Google Scholar 

  5. R.E. Block and R.L. Wilson, "The restricted simple Lie algebras with a two-dimensional Cartan subalgebra", Bull. Amer. Math. Soc. (N.S.) 1 (1979), 682–684.

    Article  MathSciNet  MATH  Google Scholar 

  6. _____, "The simple p-Lie algebras of rank two", submitted.

    Google Scholar 

  7. H.J. Chang, "Uber Wittsche Lie-Ringe", Abh. Math. Sem. Univ. Hamburg 14 (1941), 151–184.

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Jacobson, "A note on three-dimensional simple Lie algebras", J. Math. Mech. 7 (1958), 823–831.

    MathSciNet  MATH  Google Scholar 

  9. _____, Lie algebras, Interscience, New York, 1962.

    Google Scholar 

  10. V. G. Kac, "The classification of the simple Lie algebras over a field with nonzero characteristic" (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 385–408; English Transl., Math. USSR-Izv. 4 (1970), 391–413.

    MathSciNet  Google Scholar 

  11. _____, "Global Cartan pseudogroups and simple Lie algebras of characteristic p" (Russian), Uspehi Mat. Nauk 26 (1971), 199–200.

    MathSciNet  MATH  Google Scholar 

  12. _____, "Filtered Lie algebras of Cartan type" (Russian), Uspehi Mat. Nauk 29 (1974), 203–204.

    MathSciNet  Google Scholar 

  13. _____, "Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated" (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 800–838; Errata, 40 (1976), 1415; English transl., Math. USSR-Izv. 8 (1974), 801–835; Errata, 10 (1976), 1339.

    MathSciNet  Google Scholar 

  14. I. Kaplansky, "Lie algebras of characteristic p", Trans. Amer. Math. Soc. 89 (1958), 149–183.

    MathSciNet  MATH  Google Scholar 

  15. A. I. Kostrikin, "Variations modulaires sur un theme de Cartan", Actes Congres Intern. Math., Nice 1 (1970), 285–292.

    MathSciNet  Google Scholar 

  16. A. I. Kostrikin and I. R. Safarevic, "Cartan pseudogroups and Lie p-algebras" (Russian), Dokl. Akad. Nauk SSSR 168 (1966), 740–742; English transl., Soviet Math. Dokl. 7 (1966), 715–718.

    MathSciNet  Google Scholar 

  17. _____, "Graded Lie algebras of finite characterisc" (Russian), Izv. Akad. Nauk SSSR Ser. Math. 33 (1969), 251–322; English transl., Math. USSR-Izv. 3 (1969), 237–304.

    MathSciNet  Google Scholar 

  18. H. Strade, "Representations of the Witt algebra", J. Algebra 49 (1977), 595–605.

    Article  MathSciNet  MATH  Google Scholar 

  19. B. Ju. Weisfeiler, "Infinite dimensional filtered Lie algebras and their connection with graded Lie algebras" (Russian), Funkcional Anal. i Prilozen. 2 (1968), 94–95.

    Article  MathSciNet  Google Scholar 

  20. _____, "On the structure of the minimal ideal of some graded Lie algebras in characteristic p>0", J. Algebra 53 (1978), 344–361.

    Article  MathSciNet  MATH  Google Scholar 

  21. R. L. Wilson, "Nonclassical simple Lie algebras", Bull. Amer. Math. Soc. 75 (1969), 987–991.

    Article  MathSciNet  MATH  Google Scholar 

  22. _____, "A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic", J. Algebra 40 (1976), 418–465.

    Article  MathSciNet  MATH  Google Scholar 

  23. _____, "Simple Lie algebras of toral rank one", Trans. Amer. Math. Soc. 236 (1978), 287–295.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. J. Winter, "On the toral structure of Lie p-algebras", Acta Math. 123 (1969), 70–81.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rutgers University, 08903, New Brunswick, New Jersey

    Robert Lee Wilson

Authors
  1. Robert Lee Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ralph K. Amayo

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Wilson, R.L. (1981). A “new” proof of kaplansky's theorem on simple Lie algebras of rank one. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090553

Download citation

  • DOI: https://doi.org/10.1007/BFb0090553

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10573-2

  • Online ISBN: 978-3-540-38549-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation