G2 is the name of a Lie group (and also its Lie algebra). It is one of the exceptional simple Lie groups.

Table of contents
1 Roots of G2
2 Weyl/Coxeter group
3 Cartan matrix

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.







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.