Identities in Moufang sets
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- by Tom De Medts and Yoav Segev PDF
- Trans. Amer. Math. Soc. 360 (2008), 5831-5852 Request permission
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.References
- Tom De Medts and Richard M. Weiss, Moufang sets and Jordan division algebras, Math. Ann. 335 (2006), no. 2, 415–433. MR 2221120, DOI 10.1007/s00208-006-0761-8
- Kevin McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1072–1079. MR 202783, DOI 10.1073/pnas.56.4.1072
- Kevin McCrimmon, A taste of Jordan algebras, Universitext, Springer-Verlag, New York, 2004. MR 2014924
- Y. Segev, R. M. Weiss, On the action of the Hua subgroups in special Moufang sets, to appear in Math. Proc. Cambridge Philos. Soc.
- Franz Georg Timmesfeld, Abstract root subgroups and simple groups of Lie type, Monographs in Mathematics, vol. 95, Birkhäuser Verlag, Basel, 2001. MR 1852057, DOI 10.1007/978-3-0348-7594-3
- Jacques Tits, Twin buildings and groups of Kac-Moody type, Groups, combinatorics & geometry (Durham, 1990) London Math. Soc. Lecture Note Ser., vol. 165, Cambridge Univ. Press, Cambridge, 1992, pp. 249–286. MR 1200265, DOI 10.1017/CBO9780511629259.023
- Jacques Tits and Richard M. Weiss, Moufang polygons, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2002. MR 1938841, DOI 10.1007/978-3-662-04689-0
Additional Information
- Tom De Medts
- Affiliation: Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 S22, 9000 Ghent, Belgium
- MR Author ID: 701084
- ORCID: 0000-0002-9504-5353
- Email: tdemedts@cage.ugent.be
- Yoav Segev
- Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
- MR Author ID: 225088
- Email: yoavs@math.bgu.ac.il
- 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 - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 5831-5852
- MSC (2000): Primary 17C60, 20E42; Secondary 17C30
- DOI: https://doi.org/10.1090/S0002-9947-08-04414-0
- MathSciNet review: 2425693