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Infinitesimal Invariants in a Function Algebra

Published online by Cambridge University Press:  20 November 2018

Rudolf Tange
Rudolf Tange*
Affiliation:
Department of Mathematics, University of York, York, YO10 5DD, UK, e-mail: rht502@york.ac.uk
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Abstract

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Let $G$ be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let $\mathfrak{g}$ be its Lie algebra. First we extend a well-known result about the Picard group of a semi-simple group to reductive groups. Then we prove that if the derived group is simply connected and $\mathfrak{g}$ satisfies a mild condition, the algebra $K{{[G]}^{\mathfrak{g}}}$ of regular functions on $G$ that are invariant under the action of $\mathfrak{g}$ derived from the conjugation action is a unique factorisation domain.

Keywords

20G1513F15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 950 - 960
Copyright
Copyright © Canadian Mathematical Society 2012

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