On the adjoint quotient of Chevalley groups over arbitrary base schemes
| dc.creator | Chaput, Pierre-Emmanuel | |
| dc.creator | Romagny, Matthieu | |
| dc.date | 2008-05-14 | |
| dc.date.accessioned | 2026-07-07T12:18:53Z | |
| dc.date.available | 2026-07-07T12:18:53Z | |
| dc.description | For 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.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2140 | |
| dc.identifier | http://arxiv.org/abs/0805.2140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212564 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A50, 20G15 | |
| dc.title | On the adjoint quotient of Chevalley groups over arbitrary base schemes | |
| dc.type | text |