1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Killing form for gl_n

  1. Dec 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Does anybody know of a concise way to prove that the Killing form of gl_n is given by [tex] B(X,Y) = 2n Tr(X \cdot Y) - 2 Tr(X) Tr(Y)[/tex]?

    2. Relevant equations

    3. The attempt at a solution

    I believe that this can be shown by noting that a basis for gl_n is given by the matrices E_{ij} whose only nonzero entries occur in the (i,j) entries. Using this fact, one could then explicitly work out the adjoint representation. Is there a simpler way, however?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted