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A HILBERT BASIS THEOREM FOR QUANTUM GROUPS

Published online by Cambridge University Press:  01 March 1997

K. A. BROWN  and
K. R. GOODEARL
K. A. BROWN
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
K. R. GOODEARL
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
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Abstract

A noncommutative version of the Hilbert basis theorem is used to show that certain [Rscr ]-symmetric algebras S[Rscr ](V) are Noetherian. This result applies in particular to the coordinate ring of quantum matrices A[Rscr ](V) associated with an R-matrix [Rscr ] operating on the tensor square of a vector space V, to show that, under a natural set of hypotheses on [Rscr ], the algebra A[Rscr ](V) is Noetherian and its augmentation ideal has a polynormal set of generators. As a corollary we deduce that these properties hold for the generic quantized function algebras Rq [G] over any field of characteristic zero, for G an arbitrary connected, simply connected, semisimple group over [Copf ]. That Rq[G] is Noetherian recovers a result due to Joseph [10], with a different proof.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 150 - 158
Copyright
© The London Mathematical Society 1997

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