Infinitesimal invariants in a function algebra

• Main Author: Tange, R.H (Author)
• Format: Article
• Language: English
• Published: 2006.
• Subjects: Article
• Online Access: Get fulltext

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