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Fixed points of quasi-semi-simple automorphisms. (Points fixes des automorphismes quasi-semi-simples.) (French. Abridged English version) Zbl 1001.20043
Summary: Let $$\mathbf G$$ be a connected algebraic reductive group over an algebraically closed field. An algebraic automorphism $$\sigma$$ of $$\mathbf G$$ is quasi-semi-simple if it stabilises a pair of a maximal torus of $$\mathbf G$$ and a Borel subgroup of $$\mathbf G$$ containing it; then the connected component $$({\mathbf G}^\sigma)^0$$ of the fixed-point group $${\mathbf G}^\sigma$$ is a reductive group. We give an explicit description of its root system which allows us, as promised [in F. Digne, J. Michel, Ann. Sci. Éc. Norm. Supér., IV. Sér. 27, No. 3, 345-406 (1994; Zbl 0846.20040), 1.15] to (belatedly) complete the proof which was left incomplete there.

MSC:
 20G15 Linear algebraic groups over arbitrary fields 20E36 Automorphisms of infinite groups
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References:
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