Lattice (group)

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In geometry and group theory, a lattice in the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of lattice points having the following properties: Coordinate-wise addition or subtraction of two points in the lattice produces another lattice point. The lattice points are all separated by some minimum distance (isolated). Every point in the space is within some maximum distance of a lattice point. One of the simplest examples of a lattice is the square lattice, which consists of all points ( a , b ) {\displaystyle (a,b)} in the plane whose coordinates are both integers, and its higher-dimensional analogues, the integer lattices Z n {\displaystyle \mathbb...

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