 Building (mathematics)

In the context of mathematics, particularly in combinatorial geometry and geometric combinatorics, a "building" refers to a particular type of geometric structure that generalizes the concept of certain types of spaces, often associated with groups of symmetries known as "Lie groups." Buildings are combinatorial structures that can be used to study these groups and their representations. Buildings can be defined as a collection of simplices that meet specific conditions, producing a coherent geometric structure.