From http://math.ucr.edu/home/baez/week61.html" [Broken], I got the following quote

The author speaks about Lie groups, not Lie algebras. I do not understand the we can convert any representation of SO(3) into one of SU(2) part. The j=1/2 representation, the spinorial representation of SU(2) are the 2x2 Pauli matrices. But how can there be a j=1 representation, a vector representation for SU(2)? Would it still be a double cover of SO(3)? What does it look like?

EDIT. More generally,http://en.wikipedia.org/wiki/Spin_representation" [Broken] (the half-integer reps) are the representation of the spin groups. What then are the vector representation (the integer reps) of the spin groups?