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Example 1.
First initialize a Lie algebra and display the multiplication table.
Alg2 >
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| (2.1) |
Check that is an ideal and find the quotient algebra (call it Alg2) using the complementary vectors
Alg1 >
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Alg1 >
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Alg1 >
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| (2.3) |
Rerun QuotientAlgebra with the keyword argument "Matrix".
Alg1 >
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Alg2 >
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| (2.4) |
We use the DifferentialGeometrycommand Transformation to convert the matrix A into a transformation from Alg1 to the quotient algebra Alg2.
Alg1 >
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| (2.5) |
We can check that is a Lie algebra homomorphism.
Alg2 >
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We see that sends to 0, to and so on.
Alg2 >
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| (2.7) |
We can verify that [is a basis for the kernel of and that the image of is spanned by (so that is surjective).
Alg2 >
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Alg1 >
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| (2.9) |