LieAlgebras[SubalgebraNormalizer] - find the normalizer of a subalgebra
h - a list of vectors defining a subalgebra h in a Lie algebra 𝔤
k - (optional) a list of vectors defining a subalgebra k of 𝔤 containing the subalgebra h
Let 𝔤 be a Lie algebra and let h ⊂k ⊂𝔤 be subalgebras.The normalizer n of h in k is the largest subalgebra n of k which contains h as an ideal. The normalizer of h always contains h itself.
SubalgebraNormalizer(h, k) calculates the normalizer of h in the subalgebra k. If the second argument k is not specified, then the default is k =𝔤 and the normalizer of h in 𝔤 is calculated.
A list of vectors defining a basis for the normalizer of h is returned.
The command SubalgebraNormalizer is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form SubalgebraNormalizer(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-SubalgebraNormalizer(...).
First initialize a Lie algebra and display the Lie bracket multiplication table.
L1 ≔ _DG⁡LieAlgebra,Alg1,5,2,5,1,1,3,4,1,1,3,5,2,1:
Calculate the normalizer of S1 = span e3 in S2 =spane1,e3,e4.
S1 ≔ e3:S2 ≔ e1,e3,e4:
Calculate the normalizer of S3=spane2,e4 in S4=e1, e2,e4,e5.
S3 ≔ e2,e4:S4 ≔ e1,e2,e4,e5:
Calculate the normalizer of S5=spane1,e2 in the Lie algebra Alg1.
S5 ≔ e1,e2:
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