# Earthliŋ

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The Portuguese Language proposal on Area 51 could use your support. Anyone interested in the Portuguese language can follow the proposal here.

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 May11 asked Space modelled on ring May6 awarded Caucus Apr28 asked Radical of $\mathfrak{gl}_n$ Apr28 comment Find $\dim R(T)$ and $\dim N(T)$ from the matrix of a linear map $T$ Look up Gaussian elimination, e.g. on Wikipedia or YouTube. Apr28 answered Find $\dim R(T)$ and $\dim N(T)$ from the matrix of a linear map $T$ Apr28 accepted Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ Apr28 comment Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ I did the calculation. As you said it was very boring—it turns out to be a 10-dimensional subgroup of $GL(6,\mathbb R)$ times $\mathbb Z_2$ (semi-direct). Apr27 asked Solvable Lie algebra with codimension 1 ideal Apr19 comment Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ "Just compute it" isn't what I hoped for when I asked the question, but maybe the only sensible answer. Thank you for the lead, I'm giving it a try. Apr19 comment Easy problems on continuity Sorry, I only saw the word continuous, and the identity $\mathrm{cos}\tfrac1x=1-\mathrm{sin}\tfrac1{2x}$... Apr19 comment Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ @MarianoSuárez-Alvarez I gave up trying to write it as a quotient and edited the question. Apr19 revised Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ added 203 characters in body Apr19 comment Easy problems on continuity You sure? What happens with (i) when $x\to 0$? Google "cos(1/x)", Google seems to have a plotting function now. Apr18 accepted Choosing central generator for nilpotent group generated by 3 elements Apr18 awarded Teacher Apr18 comment Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ True. This seems to be less trivial than I imagined. Is $\operatorname{Aut}(\mathfrak{g\oplus g})\cap\operatorname{Aut}(\Delta\mathfrak g)$ normal in $\operatorname{Aut}(\mathfrak{g\oplus g})$? Apr18 comment Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ Yes, I mean $\operatorname{Aut}(\mathfrak{g\oplus g)/\operatorname{Aut}(\Delta g})$. Apr18 asked Automorphism group of Lie algebra $\mathfrak{g\oplus g}$ Apr18 comment Choosing central generator for nilpotent group generated by 3 elements I found a comment on this question on MO, which claims that one generator can be chosen to be central. However, I do not understand the reasoning by which the commenter deduced this fact. Could there be a simple proof for the case when the number of generators is 3? Apr18 answered Prove all neighbourhoods are open in this topology