Building (mathematics)
In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.
Read more about Building (mathematics): Overview, Definition, Elementary Properties, Connection With BN Pairs, Spherical and Affine Buildings For SLn, Classification, Applications
Famous quotes containing the word building:
“A building is akin to dogma; it is insolent, like dogma. Whether or no it is permanent, it claims permanence, like a dogma. People ask why we have no typical architecture of the modern world, like impressionism in painting. Surely it is obviously because we have not enough dogmas; we cannot bear to see anything in the sky that is solid and enduring, anything in the sky that does not change like the clouds of the sky.”
—Gilbert Keith Chesterton (1874–1936)