Timeline for A question on linear groups

6 events

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Jul 3, 2016 at 21:40	comment	added	YCor		I've downvoted your answer because it contains a mistake and you didn't edit it to fix/clarify it. You should say explicitly what you prove, namely that $\mathfrak{so}_n(\mathbf{R)})$ is a maximal subalgebra, and the consequence that $\mathrm{SO}(n)$ is maximal among closed subgroups of $\mathrm{SL}_n(\mathbf{R})$, showing in particular that the closure of $\langle \mathrm{SO}(n),t\rangle$ contains $\mathrm{SL}_n$ whenever $t$ is not a scalar multiple of an isometry.
Jun 30, 2016 at 16:06	comment	added	YCor		No, I didn't. When I say "the set of $x$ in the Lie algebra...", I mean, in the Lie algebra $\mathfrak{gl}_n$ (but indeed I didn't justify that it's a Lie subalgebra, which requires a little argument).
Jun 30, 2016 at 15:30	comment	added	Venkataramana		@Ycor; actually, your comments also assume $G$ has a Lie algebra so you have also assumed that $G$ is an analytic subgroup. So your proof is just as incomplete!
Jun 30, 2016 at 15:05	comment	added	YCor		Your proof is incomplete, since it assumes implicitly $G$ closed (or, at least, an analytic subgroup). There's some further stuff in between.
Jun 30, 2016 at 14:22	history	edited	Venkataramana	CC BY-SA 3.0	added 77 characters in body
Jun 30, 2016 at 14:15	history	answered	Venkataramana	CC BY-SA 3.0