#### Vol. 4, No. 2, 2010

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On the dimension of $H$-strata in quantum algebras

### Jason P. Bell and Stéphane Launois

Vol. 4 (2010), No. 2, 175–200
##### Abstract

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 the one hand, and the theory of deleting derivations of Cauchon on the other. We also give a formula for the dimensions of the $H$-strata described by Goodearl and Letzter. We apply the results obtained to the algebra of $m×n$ generic quantum matrices to show that the dimensions of the $H$-strata are bounded above by the minimum of $m$ and $n$, and that all values between $0$ and this bound are achieved.

##### Keywords
prime spectrum, Zariski topology, stratification, quantum matrices
Primary: 16W35
Secondary: 20G42
##### Milestones
Received: 9 March 2009
Revised: 14 October 2009
Accepted: 26 November 2009
Published: 26 January 2010
##### Authors
 Jason P. Bell Jason Bell Department of Mathematics Simon Fraser University Burnaby, BC  V5A 1S6 Canada Stéphane Launois School of Mathematics, Statistics and Actuarial science University of Kent Canterbury, Kent  CT2 7NF United Kingdom