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!

Sl(2,z) matrices with integer coefficients

  1. Aug 8, 2005 #1
    Let SL(2,Z) be the set of 2x2 matrices with integer coefficients.
    I know that SL(2,Z) is generated by S and T, where
    S= (0 -1
    1 0)
    and T= (1 1
    0 1).

    But how can I show that everyone element of G (the group generated by S and T) is in SL(2,Z)?

    Also, let FcH (upper half-plane) be defined as F= {z in C: abs(z)>1, abs(Re(z)<1/2)}.
    How can I draw a picture of F? Which linear fractional transformations correspond to S and T (as given above)?
  2. jcsd
  3. Aug 9, 2005 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Am i reading riht? tw group generrated by S and T is the set of all products of S, T and their inverses in some order some fininte number of times. the entries are boviously all integers and the derteminants all1 so of course it is in SL(2,Z)

    and the second part... well, as alwayas, draw on the regiosn where |z|=1, and |Re(z)|=1/2 and work out which region corresponds to the inequialities
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Sl(2,z) matrices with integer coefficients
  1. Matrices Question 2 (Replies: 15)