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Example 1.
First we obtain a Lie algebra of vector fields from the paper by Gonzalez-Lopez, Kamran, Olver in the DifferentialGeometry Library using the Retrieve command and then we compute the isotropy filtration.
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M >
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We calculate the isotropy filtration as a subalgebra of .
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| (2.3) |
Example 2.
We continue with Example 1. Here we calculate the isotropy filtration as a subalgebra of the abstract Lie algebra defined by . To this end, we first calculate the structure constants for and initialize the result as Alg1.
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Now re-run the IsotropyFiltration command with the third argument output = [Alg1].
Alg1 >
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We check that F does indeed define a filtration of the Lie algebra (note that there is an index shift = F[k+1]).
Alg1 >
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Alg1 >
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| (2.7) |
Alg1 >
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Alg1 >
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Alg1 >
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Alg1 >
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All these brackets can be checked at once with Query/"filtration".
Alg1 >
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