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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.
Roots of G_{2}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 groupIt's Weyl/Coxeter group is the dihedral group, D_{6}.Cartan matrixSee also Simple Lie group, Lie group, Weyl group, Dynkin diagram. | |||||||
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