Editing Building (mathematics) (section)

{{Short description|Mathematical structure}}
In [[mathematics]], a '''building''' (also '''Tits building''', named after [[Jacques Tits]]) is a combinatorial and geometric structure which simultaneously  generalizes certain aspects of [[flag manifold]]s, finite [[projective plane]]s, and [[Riemannian symmetric space]]s. Buildings were initially introduced by Jacques Tits as a means to understand the structure of [[Reductive group#Non-split reductive groups|isotropic]] [[Reductive group|reductive]] [[linear algebraic group]]s over arbitrary fields. The more specialized theory of Bruhat–Tits buildings (named also after [[François Bruhat]]) plays a role in the study of [[p-adic Lie group|{{mvar|p}}-adic Lie groups]] analogous to that of the theory of [[symmetric spaces]] in the theory of [[Lie group]]s.