On certain twin buildings over tree diagrams (Q1281147)

The classification of the finite Moufang foundations over tree diagrams relies on the fact that each finite Moufang polygon satisfies a certain property denoted (Ind). Starting with a Moufang foundation \({\mathcal F}\) over a tree diagram, the authors construct a twin building \({\mathcal B}\) and an automorphism \(\gamma\) of \({\mathcal B}\) such that the fixed point structure of \(\gamma\) in \({\mathcal B}\) is a twin building whose local structure is isomorphic to \({\mathcal F}\). Twin buildings generalize spherical buildings in a natural way. This paper is a contribution to the classification program outlined by \textit{J. Tits} [Groups, Combinatorics and Geometry, Lond. Soc. Lect. Note Ser. 165, 249-286 (1992; Zbl 0851.22023)].