Skip to main content
SpringerLink
Log in

On the identities defining a quadratic Jordan division algebra

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

Quadratic Jordan algebras are defined by identities that have to hold strictly, i.e that continue to hold in every scalar extension. In this paper we show that strictness is not required for quadratic Jordan division algebras.

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. De Medts T., Segev Y.: Identities in Moufang sets. Trans. Am. Math. Soc. 360, 5831–5852 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. De Medts T., Segev Y.: A course on Moufang sets. Innov. Incid. Geom. 9, 79–122 (2009)

    MATH  MathSciNet  Google Scholar 

  3. De Medts T., Weiss R.: Moufang sets and Jordan division algebras. Math. Ann. 335, 415–433 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. N. Jacobson, Lectures on quadratic Jordan algebras, Lectures on Mathematics and Physics. Mathematics. 45. Bombay: Tata Institute of Fundamental Research (1969).

  5. McCrimmon K.: A general theory of Jordan rings. Proc. Natl. Acad. Sci. USA 56, 1072–1079 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  6. McCrimmon K.: A taste of Jordan algebras. Springer, Berlin (2004)

    MATH  Google Scholar 

  7. McCrimmon K., Zel’manov E.: The structure of strongly prime Jordan division algebras. Adv. Math. 69, 133–222 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Segev Y.: Proper Moufang sets with Abelian root groups are special. J. Am. Math. Soc. 22, 889–908 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. F. G. Timmesfeld, Abstract root subgroups and simple groups of Lie-type, Monographs in Mathematics. 95. Basel: Birkhäuser (2001).

Download references

Author information

Authors and Affiliations

  1. Julius-Maximilian-Universität Würzburg, Emil-Fischer-Str. 30, 97074, Würzburg, Germany

    Matthias Grüninger

Authors
  1. Matthias Grüninger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthias Grüninger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grüninger, M. On the identities defining a quadratic Jordan division algebra. Arch. Math. 104, 11–24 (2015). https://doi.org/10.1007/s00013-014-0720-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-014-0720-7

Mathematics Subject Classification

Keywords

Search

Navigation