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

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.

prime spectrum, Zariski topology, stratification, quantum matrices
Mathematical Subject Classification 2000
Primary: 16W35
Secondary: 20G42
Received: 9 March 2009
Revised: 14 October 2009
Accepted: 26 November 2009
Published: 26 January 2010
Jason P. Bell
Jason Bell
Department of Mathematics
Simon Fraser University
Burnaby, BC  V5A 1S6
Stéphane Launois
School of Mathematics, Statistics and Actuarial science
University of Kent
Canterbury, Kent  CT2 7NF
United Kingdom