Algebraic Polygons Original Research Article

Algebraic Polygons Original Research Article 435-447 Linus Kramer, Katrin Tent Close Close preview | Purchase PDF (177 K) | Related articles | Related reference work articles AbstractAbstract Abstract In this paper we prove the following: Over each algebraically closed fieldKof characteristic 0 there exist precisely three algebraic polygons (up to duality), namely the projective plane, the symplectic quadrangle, and the split Cayley hexagon overK(Theorem 3.3). As a corollary we prove that every algebraic Tits system overKis Moufang and obtain the following classification: Timage. Let(G, B, N, S)be an irreducible effective spherical Tits system of rank≥2.If G is a connected algebraic group over an algebraically closed field of characteristic0,and if B is closed in G,then G is simple and B is a standard Borel subgroup of G.