Subalgebras found so far: 9
Orbit sizes: A^10_1: n/a; A^4_1: n/a; A^2_1: 6; A^1_1: 12;
Current subalgebra chain length: 0

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SetOutputFile("subalgebras_A^{1}_3");
LoadSemisimpleSubalgebras {}(AmbientDynkinType=A^{1}{}\left(3\right);CurrentChain=\left(\right);NumExploredTypes=\left(\right);NumExploredHs=\left(\right);Subalgebras=\left((DynkinType=A^{1}{}\left(1\right);ElementsCartan=\begin{pmatrix}1 & 1 & 1 \end{pmatrix};generators=\left(g{}\left(-6\right), g{}\left(6\right)\right)), (DynkinType=A^{2}{}\left(1\right);ElementsCartan=\begin{pmatrix}1 & 2 & 1 \end{pmatrix};generators=\left(g{}\left(-2\right)+g{}\left(-6\right), g{}\left(2\right)+g{}\left(6\right)\right)), (DynkinType=A^{4}{}\left(1\right);ElementsCartan=\begin{pmatrix}2 & 2 & 2 \end{pmatrix};generators=\left(g{}\left(-1\right)+g{}\left(-5\right), 2 g{}\left(1\right)+2 g{}\left(5\right)\right)), (DynkinType=A^{10}{}\left(1\right);ElementsCartan=\begin{pmatrix}3 & 4 & 3 \end{pmatrix};generators=\left(g{}\left(-1\right)+g{}\left(-2\right)+g{}\left(-3\right), 3 g{}\left(1\right)+4 g{}\left(2\right)+3 g{}\left(3\right)\right)), (DynkinType=2 A^{1}{}\left(1\right);ElementsCartan=\begin{pmatrix}1 & 1 & 1\\ 0 & 1 & 0 \end{pmatrix};generators=\left(g{}\left(-6\right), g{}\left(6\right), g{}\left(-2\right), g{}\left(2\right)\right)), (DynkinType=2 A^{2}{}\left(1\right);ElementsCartan=\begin{pmatrix}1 & 2 & 1\\ 1 & 0 & 1 \end{pmatrix};generators=\left(g{}\left(-4\right)+g{}\left(-5\right), g{}\left(4\right)+g{}\left(5\right), g{}\left(-1\right)+g{}\left(-3\right), g{}\left(1\right)+g{}\left(3\right)\right)), (DynkinType=A^{1}{}\left(2\right);ElementsCartan=\begin{pmatrix}1 & 1 & 1\\ 0 & 0 & -1 \end{pmatrix};generators=\left(g{}\left(-6\right), g{}\left(6\right), g{}\left(3\right), g{}\left(-3\right)\right)), (DynkinType=B^{1}{}\left(2\right);ElementsCartan=\begin{pmatrix}1 & 1 & 1\\ -1 & 0 & -1 \end{pmatrix};generators=\left(g{}\left(-6\right), g{}\left(6\right), g{}\left(3\right)+g{}\left(1\right), g{}\left(-3\right)+g{}\left(-1\right)\right)), (DynkinType=A^{1}{}\left(3\right);ElementsCartan=\begin{pmatrix}1 & 1 & 1\\ 0 & 0 & -1\\ 0 & -1 & 0 \end{pmatrix};generators=\left(g{}\left(-6\right), g{}\left(6\right), g{}\left(3\right), g{}\left(-3\right), g{}\left(2\right), g{}\left(-2\right)\right))\right))

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