Infinitesimal Invariants in a Function Algebra
Abstract
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 extend a well-known result about the Picard group of a semisimple group to reductive groups. 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 2006
- DOI:
- 10.48550/arXiv.math/0611438
- arXiv:
- arXiv:math/0611438
- Bibcode:
- 2006math.....11438T
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Rings and Algebras