intersection semilattice of a subspace arrangement

Let 𝒜 be a finite subspace arrangement in a finite-dimensional vector spaceMathworldPlanetmath V. The of 𝒜 is the subspace arrangement L(𝒜) defined by taking the closure ( of 𝒜 under intersections. More formally, let


Order ( the elements of L(𝒜) by reverse inclusion, and give it the structure of a join-semilattice by defining HK=HK for all H, K in L(𝒜). Moreover, the elements of L(𝒜) are naturally graded by codimension. If 𝒜 happens to be a central arrangement, its intersection semilattice is in fact a lattice, with the meet operation defined by HK=span(HK), where span(HK) is the subspacePlanetmathPlanetmath of V spanned by HK.

Title intersection semilattice of a subspace arrangement
Canonical name IntersectionSemilatticeOfASubspaceArrangement
Date of creation 2013-03-22 15:47:58
Last modified on 2013-03-22 15:47:58
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 52B99
Classification msc 52C35
Synonym intersection lattice
Synonym intersection semilattice