On the dimension of H-strata in quantum algebras

Bell, Jason; Launois, Stéphane

doi:10.2140/ant.2010.4.175

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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

DOI: 10.2140/ant.2010.4.175

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 $m \times n$ 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

Mathematical Subject Classification 2000

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

Vol. 4, No. 2, 2010