✦ LIBER ✦

Algebraic Polygons

✍ Scribed by Linus Kramer; Katrin Tent

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 178 KB
Volume: 182
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0179

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✦ Synopsis

In this paper we prove the following: Over each algebraically closed field K of Ž . characteristic 0 there exist precisely three algebraic polygons up to duality , namely the projective plane, the symplectic quadrangle, and the split Cayley Ž . hexagon over K Theorem 3.3 . As a corollary we prove that every algebraic Tits system over K is Moufang and obtain the following classification: Ž . T HEOREM. Let G, B, N, S be an irreducible effecti¨e spherical Tits system of rank G 2. If G is a connected algebraic group o¨er an algebraically closed field of characteristic 0, and if B is closed in G, then G is simple and B is a standard Borel subgroup of G.

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