Type: \(\displaystyle A^{1}_1\) (Dynkin type computed to be: \(\displaystyle A^{1}_1\))
Simple basis: 1 vectors: (1, 2, 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}: 3A^{1}_1
simple basis centralizer: 3 vectors: (0, 0, 0, 1), (0, 0, 1, 0), (1, 0, 0, 0)
Number of k-submodules of g: 18
Module decomposition, fundamental coords over k: \(\displaystyle V_{2\omega_{1}}+8V_{\omega_{1}}+9V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, 0, 0, -1)(0, 0, 0, -1)g_{-4}-\varepsilon_{3}-\varepsilon_{4}
Module 21(0, 0, -1, 0)(0, 0, -1, 0)g_{-3}-\varepsilon_{3}+\varepsilon_{4}
Module 31(-1, 0, 0, 0)(-1, 0, 0, 0)g_{-1}-\varepsilon_{1}+\varepsilon_{2}
Module 41(1, 0, 0, 0)(1, 0, 0, 0)g_{1}\varepsilon_{1}-\varepsilon_{2}
Module 52(-1, -1, -1, -1)(0, 1, 0, 0)g_{2}
g_{-11}
\varepsilon_{2}-\varepsilon_{3}
-\varepsilon_{1}-\varepsilon_{3}
Module 61(0, 0, 1, 0)(0, 0, 1, 0)g_{3}\varepsilon_{3}-\varepsilon_{4}
Module 71(0, 0, 0, 1)(0, 0, 0, 1)g_{4}\varepsilon_{3}+\varepsilon_{4}
Module 82(0, -1, -1, -1)(1, 1, 0, 0)g_{5}
g_{-10}
\varepsilon_{1}-\varepsilon_{3}
-\varepsilon_{2}-\varepsilon_{3}
Module 92(-1, -1, 0, -1)(0, 1, 1, 0)g_{6}
g_{-9}
\varepsilon_{2}-\varepsilon_{4}
-\varepsilon_{1}-\varepsilon_{4}
Module 102(-1, -1, -1, 0)(0, 1, 0, 1)g_{7}
g_{-8}
\varepsilon_{2}+\varepsilon_{4}
-\varepsilon_{1}+\varepsilon_{4}
Module 112(0, -1, 0, -1)(1, 1, 1, 0)g_{8}
g_{-7}
\varepsilon_{1}-\varepsilon_{4}
-\varepsilon_{2}-\varepsilon_{4}
Module 122(0, -1, -1, 0)(1, 1, 0, 1)g_{9}
g_{-6}
\varepsilon_{1}+\varepsilon_{4}
-\varepsilon_{2}+\varepsilon_{4}
Module 132(-1, -1, 0, 0)(0, 1, 1, 1)g_{10}
g_{-5}
\varepsilon_{2}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{3}
Module 142(0, -1, 0, 0)(1, 1, 1, 1)g_{11}
g_{-2}
\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{2}+\varepsilon_{3}
Module 153(-1, -2, -1, -1)(1, 2, 1, 1)g_{12}
h_{4}+h_{3}+2h_{2}+h_{1}
g_{-12}
\varepsilon_{1}+\varepsilon_{2}
0
-\varepsilon_{1}-\varepsilon_{2}
Module 161(0, 0, 0, 0)(0, 0, 0, 0)h_{1}0
Module 171(0, 0, 0, 0)(0, 0, 0, 0)h_{3}0
Module 181(0, 0, 0, 0)(0, 0, 0, 0)h_{4}0

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: 12
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 12
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,