G2 (mathematics)

G₂ isname ofLie group (and also its Lie algebra). Itone ofexceptional simple Lie groups.

Tablecontents

1 RootsG2 1.1 Simple roots 2 Weyl/Coxeter group 3 Cartan matrix

RootsG₂

Althoughspan2-dimensional space, it's much more symmetricconsider them as vectors in2-dimensional subspace ofthree 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 isdihedral group, D₆.

Cartan matrix

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