Ad
related to: lattice group math
Search results
Results From The WOW.Com Content Network
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
In mathematics, the term lattice group is used for two distinct notions: a lattice (group), a discrete subgroup of R n and its generalizations; a lattice ordered group, a group that with a partial ordering that is a lattice order
In mathematics, the lattice of subgroups of a group is the lattice whose elements are the subgroups of , with the partial ordering being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union , and the meet of two subgroups is their intersection .
Let be a locally compact group and a discrete subgroup (this means that there exists a neighbourhood of the identity element of such that = {}).Then is called a lattice in if in addition there exists a Borel measure on the quotient space / which is finite (i.e. (/) < +) and -invariant (meaning that for any and any open subset / the equality () = is satisfied).
Lattice (group), a repeating arrangement of points Lattice (discrete subgroup), a discrete subgroup of a topological group whose quotient carries an invariant finite Borel measure; Lattice (module), a module over a ring that is embedded in a vector space over a field; Lattice graph, a graph that can be drawn within a repeating arrangement of points
The Thompson group fixes a lattice and does preserve the Lie bracket of this lattice mod 3, giving an embedding of the Thompson group into E 8 (F 3). The embeddings of the maximal subgroups of E 8 up to dimension 248 are shown to the right.
The complete subgroup lattice for D4, the dihedral group of the square. This is an example of a complete lattice. In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum . A conditionally complete lattice satisfies at