On the dimension of H-strata in quantum matrices

Details On the dimension of H-strata in quantum matrices On the dimension of H-strata in quantum matrices

2009-02-27

arxiv.org/abs/0902.4813v2

Mathematics

Rings and Algebras

New introduction; results improved

Scientific paper

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.

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