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Query[ParabolicSubalgebra] - check if a list of vectors defines a parabolic subalgebra of a semi-simple Lie algebra
Calling Sequences
Query()
Parameters
P - a list of vectors, defining a subalgebra of a semi-simple Lie algebra
Description
Let g be a semi-simple Lie algebra. A Borel subalgebra b is any maximal solvable subalgebra. A parabolic subalgebra p is any subalgebra containing a Borel subalgebra. Alternatively, a subalgebra p is parabolic if its nilradical is the orthogonal complement of p with respect to the Killing form
This Query command returns true if the subalgebra p defined by the vectors satisfies
Examples
We check to see if 3 subalgebras of are parabolic. We construct the Lie algebra directly from its standard matrix representation.
Initialize the Lie algebra. We label the basis elements for in a manner consistent with its matrix representation.
Subalgebra 1.
Subalgebra 2.
Subalgebra 3.
See Also
DifferentialGeometry, LieAlgebras, ComplementaryBasis, Nilradical, ParabolicSubalgebra
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