TY - BOOK ID - 147839159 TI - Tits Polygons. AU - Mühlherr, Bernhard. AU - Weiss, Richard M. PY - 2022 SN - 1470470187 PB - Providence : American Mathematical Society, DB - UniCat KW - Moufang loops. KW - Jordan algebras. KW - Buildings (Group theory) KW - Graph theory. KW - Polygons. KW - Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Exceptional Jordan structures. KW - Group theory and generalizations -- Structure and classification of infinite or finite groups -- Groups with a $BN$-pair; buildings. KW - Geometry -- Finite geometry and special incidence structures -- Generalized quadrangles, generalized polygons. KW - Geometry -- Finite geometry and special incidence structures -- Buildings and the geometry of diagrams. UR - https://www.unicat.be/uniCat?func=search&query=sysid:147839159 AB - "We introduce the notion of a Tits polygon, a generalization of the notion of a Moufang polygon, and show that Tits polygons arise in a natural way from certain configurations of parabolic subgroups in an arbitrary spherical buildings satisfying the Moufang condition. We establish numerous basic properties of Tits polygons and characterize a large class of Tits hexagons in terms of Jordan algebras. We apply this classification to give a "rank 2" presentation for the group of F-rational points of an arbitrary exceptional simple group of F-rank at least 4 and to determine defining relations for the group of F-rational points of an an arbitrary group of Frank 1 and absolute type D4, E6, E7 or E8 associated to the unique vertex of the Dynkin diagram that is not orthogonal to the highest root. All of these results are over a field of arbitrary characteristic"-- ER -