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Moufang sets and jordan division algebras

Mathematische Annalen volume 335, pages 415–433 (2006)Cite this article

Abstract

We give a simple criterion which determines when a permutation group U and one additional permutation give rise to a Moufang set. We apply this criterion to show that every Jordan division algebra gives rise in a very natural way to a Moufang set, to provide sufficient conditions for a Moufang set to arise from a Jordan division algebra and to give a characterization of the projective Moufang sets over a commutative field of characteristic different from 2.

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References

  1. Hering, C., Kantor, W.M., Seitz, G.M.: Finite groups with a split BN-pair of rank 1, I. J. Algebra 20, 435–475 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  2. Károlyi, Gy., Kovács, S.J., Pálfy, P.P.: Doubly transitive permutation groups with abelian stabilizers. Aequationes Math. 39(2–3), 161–166 (1990)

    Google Scholar 

  3. Kerby, W., Wefelscheid, H.: Conditions of finiteness on sharply 2-transitive groups. Aequationes Math. 8, 287–290 (1972)

    Article  MathSciNet  Google Scholar 

  4. McCrimmon, K.: A general theory of Jordan rings. Proc. Nat. Acad. Sci. U.S.A. 56, 1072–1079 (1966)

    MATH  MathSciNet  Google Scholar 

  5. McCrimmon, K.: A Taste of Jordan Algebras. Springer-Verlag, Berlin, Heidelberg, New York, 2004

  6. Mühlherr, B., Van Maldeghem, H.: Moufang sets from groups of mixed type. in preparation

  7. Springer, T.A.: Jordan algebras and algebraic groups. Ergebnisse der Mathematik und ihrer Grenzgebiete 75. Springer-Verlag, Berlin, Heidelberg, New York, 1973

  8. Timmesfeld, F.: Abstract Root Subgroups and Simple Groups of Lie-Type. Birkhäuser-Verlag, Monographs in Mathematics 95. Basel, Berlin, Boston, 2001

  9. Tits, J.: Buildings of Spherical Type and Finite BN-Pairs. Lecture Notes in Mathematics 386, Springer-Verlag, New York, Heidelberg, Berlin, 1974

  10. Tits, J.: Twin buildings and groups of Kac-Moody type. in Groups, combinatorics & geometry (Durham, 1990), 249–286, London Math. Soc. Lecture Note Ser. 165, Cambridge Univ. Press, Cambridge, 1992

  11. Tits, J., Weiss, R.M.: Moufang Polygons, Springer Monographs in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, 2002

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 S22, 9000, Gent, Belgium

    Tom De Medts

  2. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Richard M. Weiss

Authors
  1. Tom De Medts
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  2. Richard M. Weiss
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Corresponding author

Correspondence to Tom De Medts.

Additional information

The first author is a Postdoctoral Fellow of the Research Foundation – Flanders (Belgium) (FWO-Vlaanderen).

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De Medts, T., Weiss, R. Moufang sets and jordan division algebras. Math. Ann. 335, 415–433 (2006). https://doi.org/10.1007/s00208-006-0761-8

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  • DOI: https://doi.org/10.1007/s00208-006-0761-8

Mathematics Subject Classification (2000)

  • 17C30
  • 17C60
  • 20E42