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Homework Help: Isomorphism of orientation preserving rigid motions

  1. Feb 18, 2010 #1
    Find an isomorphism from the subgroup of GL2(C) of the form
    [tex]
    \begin{pmatrix}
    a & b\\
    0 & 1
    \end{pmatrix}

    ,\left | a \right |=1
    [/tex]


    to the group of orientation preserving rigid motions.



    *The problem is from Artin's Algebra Chapter5
     
  2. jcsd
  3. Feb 18, 2010 #2
    How about using the argument (angle) of a to represent rotation of the rigid object around the z-axis, and use the real and imaginary parts of b to represent an arbitrary translation along the (x,y) plane? These are orientation preserving motions of rigid objects in R^3.

    Torquil
     
  4. Feb 18, 2010 #3

    Redbelly98

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  5. Feb 19, 2010 #4
    [tex]
    \begin{pmatrix}
    a & b\\
    0 & 1
    \end{pmatrix}

    ,\left | a \right |=1
    [/tex]

    goes to az + b.
     
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