Query[Solvable] - check if a Lie algebra is solvable
Calling Sequences
Query(Alg, "Solvable")
Query(S, "Solvable")
Parameters
Alg - (optional) name or string, the name of an initialized Lie algebra
S - a list of vectors defining a basis for a subalgebra
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Description
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A Lie algebra g is solvable if the k-th element D^k(g) in the derived series for g is 0 for some k >= 0.
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Every nilpotent Lie algebra is solvable.
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Query(Alg, "Solvable") returns true if Alg is a solvable Lie algebra and false otherwise. If the algebra is unspecified, then Query is applied to the current algebra.
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Query(S, "Solvable") returns true if the subalgebra S is a solvable Lie algebra and false otherwise.
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The command Query is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form Query(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-Query(...).
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Examples
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Example 1.
We initialize three different Lie algebras.
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| (2.2) |
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Alg1 and Alg2 are solvable but Alg3 is not. (Alg1 is actually nilpotent while Alg3 is semisimple.)
Alg3 >
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Alg1 >
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| (2.5) |
Alg2 >
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The subalgebra S1 = [z1, z2] is a solvable subalgebra of Alg3. (The algebra Alg3 is SL(2, R) and S1 is a Borel subalgebra.)
Alg3 >
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| (2.7) |
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