Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dimension formulas for Lie algebras

  1. May 8, 2012 #1
    Hi.

    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!
     
  2. jcsd
  3. May 8, 2012 #2


    I'm not sure, but I'd say most decent books in Lie Algebras mention this. Anyway, Humphreys's "Int. to Lie Algebras and Repres. Theory" does.

    DonAntonio
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dimension formulas for Lie algebras
  1. Lie algebra concept (Replies: 1)

Loading...