1. Not finding help here? Sign up for a free 30min 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!

Question about basis of Lie algebra/tangent

  1. Jun 19, 2008 #1
    Hi, I'm a newbie here and I would like to kindly ask for your collective wisdom on this forum.

    I am working on a computational technique to describe a time series data on U(2), for now. Given two points x and y in U(2), I can take a matrix log of x'y to find the tangent emanating from x to y. Using the one-parameter exponential map, I can find the points along the geodesic using the so obtained tangent. My thought was to have a basis representation of the tangent space so as to come up with quantized approximate tangent which can best (in terms of geodesic distance) describe the computed tangent.

    Intuitively, I want to form a grid of tangent directions which could be used at any point on U(2).

    Does there exist such a basis? Where can I look for such formulations?

    I apologize in advance if this a naive thought as I have no formal training in Lie group/Lie algebra. Thanks in advance for any help.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Question about basis of Lie algebra/tangent
  1. Lie algebra question (Replies: 4)

  2. Lie algebra (Replies: 1)