Can an anisotropic reductive group admit a Tits system?

Details Can an anisotropic reductive group admit a Tits system? Can an anisotropic reductive group admit a Tits system?

2009-08-18

arxiv.org/abs/0908.2577v1

Mathematics

Group Theory

10 pages, to appear in Pure and Applied Mathematics Quarterly (PAMQ)

Scientific paper

Seeking for a converse to a well-known theorem by Borel-Tits, we address the question whether the group of rational points G(k) of an anisotropic reductive k-group may admit a split spherical BN-pair. We show that if k is a perfect field or a local field, then such a BN-pair must be virtually trivial. We also consider arbitrary compact groups and show that the only abstract BN-pairs they can admit are spherical, and even virtually trivial provided they are split.

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