g: A^{1}_1. There are 2 table entries (= 0 larger than the Cartan subalgebra + the Cartan subalgebra + the full subalgebra).
Type k_{ss}: A^{1}_1 (Full subalgebra)
Type C(k_{ss})_{ss}: 0
Type k_{ss}: 0 (Cartan subalgebra)
Type C(k_{ss})_{ss}: A^{1}_1
There are 2 parabolic, 0 pseudo-parabolic but not parabolic and 0 non pseudo-parabolic root subsystems.The roots needed to generate the root subsystems are listed below. ["parabolic","0", []], ["parabolic","A^{1}_1", [[1]]]LaTeX table with root subalgebra details. \documentclass{article}
\usepackage{longtable, amssymb, lscape}
\begin{document}
Lie algebra type: $A^{1}_1$. There are 2 table entries (= 0 larger than the Cartan subalgebra + the Cartan subalgebra + the full subalgebra).
Let $\mathfrak g$ stand for the type of the regular subalgebra and $C(\mathfrak g)$ for the type of the centralizer. Let $r$ stand for the rank of $\mathfrak g$, let $r_c$ stand for the rank of the semisimple part of the centralizer, let $p$ stand for the number of positive roots of $\mathfrak g$, let $q$ stand for the number of positive roots of the centralizer, and let $m$ stand for the number of $A_1$ components (of all root lengths) of $\mathfrak g$. \begin{longtable}{cccccccc}
$\mathfrak g$ & $C(\mathfrak g)$& $p$ & $q$& $m$& $r$ & $c_r$ \\\endhead
$A^{1}_1$&$0$&$1$&$0$&$1$&$1$&$0$&\\
$0$&$A^{1}_1$&$0$&$1$&$0$&$0$&$1$&\\
\end{longtable}
\end{document}