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Moufang sets and jordan division algebras

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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Correspondence to Tom De Medts.

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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