Geodesic
Infinitesimal Invariants in a Function Algebra
Canadian journal of mathematics, Tome 61 (2009) no. 4, pp. 950-960

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2009-048-6
Mots-clés : 20G15, 13F15 
Tange, Rudolf. Infinitesimal Invariants in a Function Algebra. Canadian journal of mathematics, Tome 61 (2009) no. 4, pp. 950-960. doi: 10.4153/CJM-2009-048-6
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