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

 

Descent of affine buildings - I. Large minimal angles


Authors: Bernhard Mühlherr, Koen Struyve and Hendrik Van Maldeghem
Journal: Trans. Amer. Math. Soc. 366 (2014), 4345-4366
MSC (2010): Primary 51E24, 20E42
Published electronically: April 16, 2014
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Abstract: In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture concerning the existence of affine buildings arising from such groups defined over a (skew) field with a complete valuation, as proposed by Jacques Tits.

This first part lays the foundations for our approach and deals with the `large minimal angle' case.


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Additional Information

Bernhard Mühlherr
Affiliation: Mathematics Institute, Universitat Giessen, 35392 Giessen, Germany

Koen Struyve
Affiliation: Department of Pure Mathematics, Ghent University, B-9000 Ghent, Belgium

Hendrik Van Maldeghem
Affiliation: Department of Pure Mathematics, Ghent University, B-9000 Ghent, Belgium

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05985-0
PII: S 0002-9947(2014)05985-0
Received by editor(s): January 19, 2012
Received by editor(s) in revised form: September 23, 2012, and October 15, 2012
Published electronically: April 16, 2014
Additional Notes: The second author was supported by the Fund for Scientific Research – Flanders (FWO - Vlaanderen)
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.