In [7] the q tetrahedron algebra ¢ q was introduced as a q analogue of the universal enveloping algebra of the three point loop algebra sl 2 ª C[t, t 1 , (t 1) 1 ]. In this paper the relation between finite dimensional ¢ q modules and finite dimensional modules for U q (L(sl 2 )), a q analogue of the loop algebra L(sl 2 ), is studied. A connection between the ¢ q module structure and L-operators for U q (L(sl 2 )) is also discussed.