The symplectic ideal and a double centraliser theorem
The symplectic ideal and a double centraliser theorem
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.
15pp
Tange, Rudolf
a406e813-1bce-49f1-8d3d-07dfdd129a47
2007
Tange, Rudolf
a406e813-1bce-49f1-8d3d-07dfdd129a47
Tange, Rudolf
(2007)
The symplectic ideal and a double centraliser theorem.
Journal of the London Mathematical Society, .
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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Published date: 2007
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Local EPrints ID: 45977
URI: http://eprints.soton.ac.uk/id/eprint/45977
ISSN: 0024-6107
PURE UUID: 4aab40e4-bf02-4591-8edc-208f257a1a88
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Date deposited: 03 May 2007
Last modified: 15 Mar 2024 09:15
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Author:
Rudolf Tange
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