Type: \(\displaystyle 0\) (Dynkin type computed to be: \(\displaystyle 0\))
Simple basis: 0 vectors:
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}: A^{1}_1
simple basis centralizer: 1 vectors:
(1)
Number of k-submodules of g: 3 Module decomposition, fundamental coords over k: \(\displaystyle 3V_{0}\)
g/k k-submodules
id
size
b\cap k-lowest weight
b\cap k-highest weight
Module basis
Weights epsilon coords
Module 1
1
(-1)
(-1)
g_{-1}
-\varepsilon_{1}+\varepsilon_{2}
Module 2
1
(1)
(1)
g_{1}
\varepsilon_{1}-\varepsilon_{2}
Module 3
1
(0)
(0)
h_{1}
0
Information about the subalgebra generation algorithm. Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 0 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 This subalgebra is not parabolically induced by anyone Potential Dynkin type extensions: A^{1}_1,