On the dimension of H-strata in quantum matrices

We study the topology of the prime spectrum of an algebra supporting a rational torus action. More precisely, we study inclusions between prime ideals that are torus-invariant using the $H$-stratification theory of Goodearl and Letzter on one hand and the theory of deleting derivations of Cauchon on the other. We apply the results obtained to the algebra of $m \times n$ generic quantum matrices to show that the dimensions of the $H$-strata described by Goodearl and Letzter are bounded above by the minimum of $m$ and $n$, and that moreover all the values between 0 and this bound are achieved.Comment: New introduction; results improve

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