Moufang Polygons

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The book explores spherical buildings, which are combinatorial simplicial complexes linked to exceptional complex Lie groups through incidence geometries. It delves into the definitions of chamber systems and related concepts like "rank" and "thick." The theory extends to simple algebraic groups over arbitrary fields, associating each with a thick irreducible spherical building. A key theorem states that for rank three or higher, every thick irreducible spherical building is either classical, algebraic, or mixed, with mixed buildings connecting to groups defined over pairs of fields.