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Example 1.
We calculate the simple roots for the Lie algebra This is the 36-dimensional Lie algebra of matrices which are skew-symmetric with respect to the skew form
We use the command SimpleLieAlgebraData to obtain the structure equations for this Lie algebra.
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The following diagonal elements define a Cartan subalgebra. (This can be calculated using the command CartanSubalgebra).
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| (2.2) |
Here is the corresponding root space decomposition.
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| (2.3) |
We calculate the positive roots for .
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The rank of is 4 so we should find 4 positive roots.
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We check that the positive roots are positive integer linear combinations of the simple roots with the GetComponents command.
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| (2.4) |