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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

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field . Tits demonstrated how to every such group G one can associate a simplicial complex Δ   =   Δ( G ) with an action of G , called the spherical building of G . The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion. By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at his first defin

A building is a constructed object intended for occupancy by humans or animals.

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