528 research outputs found
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 -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 generic
quantum matrices to show that the dimensions of the -strata described by
Goodearl and Letzter are bounded above by the minimum of and , 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
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 .Comment: 15 pages; to appear in Glasgow Mathematical Journa
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