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- W2898347005 abstract "We study a relative variant of Serre's notion of $G$-complete reducibility for a reductive algebraic group $G$. We let $K$ be a reductive subgroup of $G$, and consider subgroups of $G$ which normalise the identity component $K^{circ}$. We show that such a subgroup is relatively $G$-completely reducible with respect to $K$ if and only if its image in the automorphism group of $K^{circ}$ is completely reducible. This allows us to generalise a number of fundamental results from the absolute to the relative setting. We also derive analogous results for Lie subalgebras of the Lie algebra of $G$, as well as 'rational' versions over non-algebraically closed fields." @default.
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- W2898347005 date "2018-10-29" @default.
- W2898347005 modified "2023-09-27" @default.
- W2898347005 title "Relative complete reducibility and normalised subgroups" @default.
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