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 × 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.