LieAlgebras[DerivedAlgebra] - find the derived algebra of a Lie algebra
Calling Sequences
DerivedAlgebra(LieAlgName)
DerivedAlgebra(S)
Parameters
LieAlgName - (optional) name or string, the name of a Lie algebra g
S - a list of vectors defining a basis for a subalgebra of g
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Description
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The derived algebra of a Lie algebra g is the span of the set of vectors [x, y] for all x, y in g. It is an ideal in g.
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DerivedAlgebra(LieAlgName) calculates the derived algebra of the Lie algebra g defined by LieAlgName. If no argument is given, then the derived algebra of the current Lie algebra is found.
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DerivedAlgebra(S) calculates the derived algebra of the Lie subalgebra S (viewed as a Lie algebra in its own right).
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A list of vectors defining a basis for the derived algebra of g (or S) is returned. If the derived algebra of g is trivial, then an empty list is returned.
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The command DerivedAlgebra is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form DerivedAlgebra(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-DerivedAlgebra(...).
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Examples
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Example 1.
First we initialize a Lie algebra.
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We calculate the derived algebra of Alg1.
Alg1 >
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We calculate the derived algebra of the subalgebra [e1, e2, e4].
Alg1 >
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| (2.3) |
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