G2 (math)
G2 is the name of a Lie group (and also its Lie algebra). It is one of the exceptional simple Lie groups.
Roots of G2
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)
Simple roots
(0,1,-1), (1,-2,1)
Weyl/Coxeter group
It's Weyl/Coxeter group is the dihedral group, D6.
Cartan matrix
See also Simple Lie group, Lie group, Weyl group, Dynkin diagram.
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