Classification and Construction of Buildings

Abstract

Abstract The purpose of this article is to give some feeling for what a building is, to discuss their classification, their construction, and something of their local structure. For more details two recent books, [Br] and [R2], are available, both published in 1989, plus a survey article [R3] which contains an introductory treatment of the subject.As is well known, the theory of buildings was introduced, and has been largely developed, by Jacques Tits. Its original purpose was to provide an understanding of the analogues of the simple Lie groups, and particularly the exceptional groups, over an arbitrary field, and in this respect it has been brilliantly successful. The theory of spherical buildings and their classification [T2] was the result, but things by no means stop there. Work of lwahori and Matsumoto [IM] gave us affine buildings; the general theory of affine buildings was then developed by Bruhat and Tits [BT], and a classification was accomplished by Tits [T7].