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
Description
Examples
MinimalIdeal(S) calculates the smallest ideal J containing the list of vectors S in an Lie algebra 𝔤.
A list of vectors giving a basis for J is returned.
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(...).
withDifferentialGeometry:withLieAlgebras:
Example 1.
First initialize a Lie algebra and display the multiplication table.
L1≔_DGLieAlgebra,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:
DGsetupL1:
MultiplicationTableLieBracket
e1,e5=2e1,e2,e3=e1,e2,e5=e2+e3,e3,e5=e3,e4,e5=2e4
Find the minimal ideal containing the vectors e1, e3.
S1≔e1,e3:
I1≔MinimalIdealS1
I1 ≔ e1,e3
Find the minimal ideal containing the vectors e2, e4.
S2≔e2,e4:
I2≔MinimalIdealS2
I2 ≔ e1,e2,e3,e4
QueryS2,Ideal
false
QueryI2,Ideal
true
See Also
DifferentialGeometry
LieAlgebras
MinimalSubalgebra
MultiplicationTable
Query[Ideal]
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