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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Identities in Moufang sets


Authors: Tom De Medts and Yoav Segev
Journal: Trans. Amer. Math. Soc. 360 (2008), 5831-5852
MSC (2000): Primary 17C60, 20E42; Secondary 17C30
Published electronically: April 16, 2008
MathSciNet review: 2425693
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Abstract: Moufang sets were introduced by Jacques Tits as an axiomatization of the buildings of rank one that arise from simple algebraic groups of relative rank one. These fascinating objects have a simple definition and yet their structure is rich, while it is rigid enough to allow for (at least partial) classification. In this paper we obtain two identities that hold in any Moufang set. These identities are closely related to the axioms that define a quadratic Jordan algebra. We apply them in the case when the Moufang set is so-called special and has abelian root groups. In addition we push forward the theory of special Moufang sets.


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Additional Information

Tom De Medts
Affiliation: Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 S22, 9000 Ghent, Belgium
Email: tdemedts@cage.ugent.be

Yoav Segev
Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
Email: yoavs@math.bgu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04414-0
PII: S 0002-9947(08)04414-0
Keywords: Moufang set, special, rank one group, Jordan algebra
Received by editor(s): September 7, 2006
Published electronically: April 16, 2008
Additional Notes: The first author was a postdoctoral fellow of the Research Foundation - Flanders (Belgium) (F.W.O.-Vlaanderen).
The second author was partially supported by BSF grant no. 2004-083
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.