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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Van Steen, K. Characterizations by Automorphism Groups of Some Rank 3 Buildings, III. Moufang-Like Conditions. Geometriae Dedicata 74, 225–240 (1999). https://doi.org/10.1023/A:1005005214943
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DOI: https://doi.org/10.1023/A:1005005214943