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Infinitesimal Invariants in a Function Algebra
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2012
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