On the adjoint quotient of Chevalley groups over arbitrary base schemes

dc.creatorChaput, Pierre-Emmanuel
dc.creatorRomagny, Matthieu
dc.date2008-05-14
dc.date.accessioned2026-07-07T12:18:53Z
dc.date.available2026-07-07T12:18:53Z
dc.descriptionFor a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W, we show that the Chevalley morphism t/W -> g/G is an isomorphism except for the group Sp_{2n} over a base with 2-torsion. In this case this morphism is only dominant and we compute it explicitly. We compute the adjoint quotient in some other classical cases, yielding examples where the formation of the quotient g -> g/G commutes, or does not commute, with base change on S.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0805.2140
dc.identifierhttp://arxiv.org/abs/0805.2140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212564
dc.subjectAlgebraic Geometry
dc.subject13A50, 20G15
dc.titleOn the adjoint quotient of Chevalley groups over arbitrary base schemes
dc.typetext

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