intersection semilattice of a subspace arrangement
Let be a finite subspace arrangement in a
finite-dimensional vector space .
The of
is the subspace
arrangement defined by taking the
closure (http://planetmath.org/ClosureAxioms)
of under intersections. More formally, let
Order (http://planetmath.org/Poset) the elements of
by reverse inclusion,
and give it the structure of a join-semilattice by defining
for all , in .
Moreover, the elements of are naturally
graded by codimension. If
happens to be a central arrangement, its intersection
semilattice is in fact a lattice, with the meet operation
defined by , where
is the subspace of spanned by
.
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 |