Automorphisms of quantum matrices

We study the automorphism group of the algebra \oqmn of $n \times n$ generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transposition and the subgroup of those automorphisms acting on the canonical generators of \oqmn by multiplication by scalars. Moreover, we prove this conjecture in the case when $n=3$.Comment: 15 pages; to appear in Glasgow Mathematical Journa