Characterizations by Automorphism Groups of Some Rank 3 Buildings, III. Moufang-Like Conditions |
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Authors: | K. Van Steen |
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Affiliation: | (1) Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, 9000 Gent, Belgium |
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Abstract: | In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type Ã2 satisfying the root-Moufang condition are Bruhat–Tits buildings. Also, every rank 3 affine building satisfying the p-adic Moufang condition is a Bruhat-Tits building. We motivate the introduction of the new conditions by showing that all Bruhat– Tits Ã2-buildings satisfy the root-Moufang condition, and that the Ã2-buildings over a p-adic field also satisfy the p-adic Moufang condition. Another application of the p-adic Moufang condition is given in Part IV of this paper. |
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Keywords: | Moufang condition p-adic affine building Bruhat– Tits building Hjelmslev plane. |
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