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LieAlgebras[MinimalIdeal] - find the smallest ideal containing a given set of vectors
Calling Sequences
MinimalIdeal(S)
Parameters
S - a list of vectors in a Lie algebra
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Description
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MinimalIdeal(S) calculates the smallest ideal containing the list of vectors S.
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A list of vectors is returned.
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The command MinimalIdeal is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form MinimalIdeal(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-MinimalIdeal(...).
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Examples
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Example 1.
First initialize a Lie algebra and display the multiplication table.
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![L1 := _DG([["LieAlgebra", Alg1, [5]], [[[1, 5, 1], 2], [[2, 3, 1], 1], [[2, 5, 2], 1], [[2, 5, 3], 1], [[3, 5, 3], 1], [[4, 5, 4], 2]]])](/support/helpjp/helpview.aspx?si=6600/file05818/math49.png)
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Alg1 >
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![[[e1, e5] = 2*e1, [e2, e3] = e1, [e2, e5] = e2+e3, [e3, e5] = e3, [e4, e5] = 2*e4]](/support/helpjp/helpview.aspx?si=6600/file05818/math58.png)
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Find the minimal ideal containing the vectors [e1, e3].
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Alg1 >
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![S1 := [e1, e3]](/support/helpjp/helpview.aspx?si=6600/file05818/math68.png)
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Alg1 >
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![I1 := [e1, e3]](/support/helpjp/helpview.aspx?si=6600/file05818/math75.png)
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Find the minimal ideal containing the vectors [e2, e4].
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Alg1 >
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![S2 := [e2, e4]](/support/helpjp/helpview.aspx?si=6600/file05818/math85.png)
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Alg1 >
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![I2 := [e1, e2, e3, e4]](/support/helpjp/helpview.aspx?si=6600/file05818/math90.png)
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Alg1 >
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| (2.4) |
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Alg1 >
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| (2.5) |
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