Hi.(adsbygoogle = window.adsbygoogle || []).push({});

1. Can anyone definitively tell me what the dimension formula for the classical Lie algebras?

For example, I know for SO(2n) or D_n, the dimension formula is

SO(N)--> (N*(N-1))/2

E.g. SO(8) is 8*7/2 = 28.

Ok, so what about SU(N+1) i.e. A_n, SO(2n+1) i.e. B_N and Sp(n) i.e. C_n ?

2. I have (using # of simple roots = the rank )

that # total roots = dim (above) - rank

and therefore the # of positive roots is half of this quantity (i.e. (dim-rank)/2 )

Any help would be great. Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Dimension formulas for Lie algebras

**Physics Forums | Science Articles, Homework Help, Discussion**