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

Lorentzian lie algebra

  1. Jan 20, 2016 #1
    Hi everybody,

    Let G a four dimmensionnal Lie group with g as lie algebra. Let T1 ... T4 the four generator. I would like to find à lorentzian scalar product (1-3 Signature) on it and left invariant. A classical algebra take tr (AB^t) as scalar product but I don't find à lorentzian équivalent. Did it contraint the generator or the structure constant to respect some criterion ?

    Thanks for your answer

  2. jcsd
  3. Jan 25, 2016 #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?
  4. Jan 25, 2016 #3


    User Avatar
    2017 Award

    Staff: Mentor

    I've read your post now several times. I'd like to help you but I don't understand it. The ##T_i## are generators of ##g## or of ##G##? What do you mean by a left invariant scalar product? And Lorentzian in this context means exactly what? Since a four dimensional Lie Algebra isn't semisimple I have difficulties to understand which bilinear form you're looking for.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook