How to find 3D representation of SU(2)

[lonewolf219]

Homework Statement

Find the 3D representation of what I think are the commutators [T_a,T_b] for the SU(2) group

Homework Equations

I think the generators(X_i) in SU(2) group are the 3 Pauli matrices, which are 2X2 matrices... I assume I need to find the matrices for these generators as 3x3?

The Attempt at a Solution

I think the equation exp^(i*alpha_i*X_i) determines what the elements of the group are...
[T_a,T_b)=T_a*T_b - T_b*T_a is the commutator
Since there are 3 generators, does that also mean there should be three matrices in 3X3 representation?

Do I sound confused?

 

[sgd37]

http://www.physics.rutgers.edu/~steves/502/Lectures_Final/Lec03_SU(2).pdf

page 13

 

[lonewolf219]

A huge thanks to you, sgd37! No more tears!