Infinitesimal invariants in a function algebra
Infinitesimal invariants in a function algebra
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.
Tange, R.H.
f875b810-3e2a-42ba-acd8-236b5dca9929
Tange, R.H.
f875b810-3e2a-42ba-acd8-236b5dca9929
Tange, R.H.
(2006)
Infinitesimal invariants in a function algebra.
Canadian Journal of Mathematics.
(In Press)
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 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.
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Submitted date: 2006
Accepted/In Press date: 2006
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Local EPrints ID: 43536
URI: http://eprints.soton.ac.uk/id/eprint/43536
PURE UUID: 0ff68bb3-1b22-4b3a-84f0-e882098e22e4
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Date deposited: 23 Jan 2007
Last modified: 15 Mar 2024 08:55
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Author:
R.H. Tange
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