Lattice (group)

In mathematics, especially in geometry and group theory, a lattice in is a subgroup of which is isomorphic to , and which spans the real vector space . In other words, for any basis of , the subgroup of all linear combinations with integer coefficients forms a lattice. A lattice may be viewed as a regular tiling of a space by a primitive cell.

Lattices have many significant applications in pure mathematics, particularly in connection to Lie algebras, number theory and group theory. They also arise in applied mathematics in connection with coding theory, in cryptography because of conjectured computational hardness of several lattice problems, and are used in various ways in the physical sciences. For instance, in materials science and solid-state physics, a lattice is a synonym for the "frame work" of a crystalline structure, a 3-dimensional array of regularly spaced points coinciding in special cases with the atom or molecule positions in a crystal. More generally, lattice models are studied in physics, often by the techniques of computational physics.

Lattice group

In mathematics, the term lattice group is used for two distinct notions:

Lattice Group

Lattice Group plc was a leading British gas transmission business. It was listed on the London Stock Exchange and was a constituent of the FTSE 100 Index.

History

The Company was established in 2000 when BG Group demerged its UK gas transmission business, formerly known as Transco, and named it Lattice Group.

In October 2002 Lattice Group merged with National Grid plc to form National Grid Transco (although in 2005 the merged entity reverted to the name National Grid plc).

Operations

As well as the UK gas transmission network, Lattice Group owned a telecoms business known as 186k.

References