Journal of the Ramanujan Mathematical Society

V. Chernousov ¹, P. Gille ², A. Pianzola ³

Affiliations
1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, CA
2 UMR 5208 du CNRS-Institut Camille Jordan-Universit´e Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, FR
3 Centro de Altos Estudios en Ciencia Exactas, Avenida de Mayo 866, (1084) Buenos Aires, AR

Abstract

We define and study the Whitehead group of isotropic (almost) simple simply connected group schemes over Laurent polynomial rings k[t^±1], where k is a field of characteristic 0. Our motivation for doing this comes from infinite dimensional Lie theory.

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P. Gille ¹

Affiliations
1 Philippe Gille, UMR 8628 Du C.N.R.S., Mathematiques, Batiment 425, Universite De Paris-Sud, F-91405 Orsay, FR

Abstract

Let G/k be a semisimple algebraic group defined over a field k with separable closure k_s. Let T a maximal k-torus of G. The Galois action on the ischolar_main system Φ(G_ks,T_ks) provides an invariant in Galois cohomology, we call it the type of T in G. We show that all possible type occur for maximal tori of quasi-split semisimple groups.

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