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

How to compute the norm of a root from the Cartan matrix?

  1. Dec 6, 2014 #1
    Hello!

    As far as I understand, the Cartan matrix is associated with a unique semi simple algebra. How can we compute the norm of a root α from it since its components are invariant under rescaling (if all the simple roots are multiplied by the same constant, the Cartan matrix remains unchanged) ?

    The square norm of the root is [itex]α(H_α)[/itex] where [itex]H_α[/itex] is such that [itex]Tr(ad (H_α) ad (h))=α(h)[/itex] for any h in the cartan subalgebra, so it seems to me that there is no freedom for choosing the norm

    Thanks!
     
  2. jcsd
  3. Dec 11, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to compute the norm of a root from the Cartan matrix?
Loading...