A class of left quantum groups modeled after SLq(n)

For each n≥2, we construct a left quantum group, i.e., a left Hopf algebra SL̃q(n) generated by comatrix units Xij, 1≤i,j≤n, which has a left antipode but no right antipode. The quantum special linear group SLq(n) is a homomorphic image of SL̃q(n).