Type: \(\displaystyle A^{1}_1\) (Dynkin type computed to be: \(\displaystyle A^{1}_1\))
Simple basis: 1 vectors: (1, 1)
Simple basis epsilon form:
Simple basis epsilon form with respect to k:
Number of outer autos with trivial action on orthogonal complement and extending to autos of ambient algebra: 0
Number of outer autos with trivial action on orthogonal complement: 0.
C(k_{ss})_{ss}: 0
simple basis centralizer: 0 vectors:

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Number of k-submodules of g: 4
Module decomposition, fundamental coords over k: \(\displaystyle V_{2\omega_{1}}+2V_{\omega_{1}}+V_{0}\)
g/k k-submodules

id	size	b\cap k-lowest weight	b\cap k-highest weight	Module basis	Weights epsilon coords
Module 1	2	(0, -1)	(1, 0)	g_{1} g_{-2}	\varepsilon_{1}-\varepsilon_{2} -\varepsilon_{2}+\varepsilon_{3}
Module 2	2	(-1, 0)	(0, 1)	g_{2} g_{-1}	\varepsilon_{2}-\varepsilon_{3} -\varepsilon_{1}+\varepsilon_{2}
Module 3	3	(-1, -1)	(1, 1)	g_{3} h_{2}+h_{1} g_{-3}	\varepsilon_{1}-\varepsilon_{3} 0 -\varepsilon_{1}+\varepsilon_{3}
Module 4	1	(0, 0)	(0, 0)	h_{2}-h_{1}	0

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Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 1
Heirs rejected due to not being maximally dominant: 1
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 1
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by 0
Potential Dynkin type extensions: A^{1}_2, 2A^{1}_1,