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GradedLieAlgebras :: subalgTableLie

subalgTableLie -- a table of dimensions of a Lie subalgebra of a Lie algebra

Synopsis

Description

The subalgebra is the least subspace containing the generators in genlist and which is closed under Lie multiplication and the differential. The columns are referring to the degree, indexed from 1, and the rows are referring to the homological degree, indexed from 0.

i1 : holonomyLie{{a1,a2,a3},{a1,a4,a5},{a2,a4,a6},{a3,a5,a6}}

o1 = LieAlgebra{...13...}

o1 : LieAlgebra
i2 : subalgTableLie(5,{a1,a2,a4})

o2 = | 3 3 8 18 48 |
     | 0 0 0 0  0  |
     | 0 0 0 0  0  |
     | 0 0 0 0  0  |
     | 0 0 0 0  0  |

              5        5
o2 : Matrix ZZ  <--- ZZ
i3 : subalgTableLie(5,{a3,a5})

o3 = | 2 1 2 3 6 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |

              5        5
o3 : Matrix ZZ  <--- ZZ
i4 : dimTableLie 5

o4 = | 6 4 10 21 54 |
     | 0 0 0  0  0  |
     | 0 0 0  0  0  |
     | 0 0 0  0  0  |
     | 0 0 0  0  0  |

              5        5
o4 : Matrix ZZ  <--- ZZ

See also

Ways to use subalgTableLie :