# G2 (mathematics)

**G**_{2} is the name of a

Lie group (and also its

Lie algebra). It is one of the exceptional simple Lie groups.

Although they span a 2-dimensional space, it's much more symmetric to consider them as

vectors in a 2-dimensional subspace of a three dimensional space.

(1,-1,0),(-1,1,0)

(-1,0,1),(1,0,-1)

(0,1,-1),(0,-1,1)

(2,-1,-1),(-2,1,1)

(-1,2,-1),(1,-2,1)

(-1,-1,2),(1,1,2)

(0,1,-1), (1,-2,1)

It's Weyl/

Coxeter group is the

dihedral group, D

_{6}.

See also Simple Lie group, Lie group, Weyl group, Dynkin diagram.