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kernel(LieDerivation) -- make the kernel of a map

Description

The optional input given above is not relevant for Lie algebras. If $d$ commutes with the differentials in the source and target of $d$, then the output is of type LieSubAlgebra. Otherwise, the output is of type LieSubSpace.

i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
            Signs=>{1,1,1},LastWeightHomological=>true)

o1 = L

o1 : LieAlgebra
 
i2 : D= differentialLieAlgebra({0_L,a a,a b})

o2 = D

o2 : LieAlgebra
 
i3 : Q=D/{b b+4 a c}

o3 = Q

o3 : LieAlgebra
 
i4 : d=differential Q

o4 = d

o4 : LieDerivation
 
i5 : Z=kernel d

o5 = Z

o5 : LieSubAlgebra
 
i6 : C=cycles Q

o6 = C

o6 : LieSubAlgebra
 
i7 : dims(8,Z)

o7 = | 1 1 0 0 0 0 0 0 |
     | 0 0 1 1 1 1 1 1 |
     | 0 0 0 0 0 0 1 2 |
     | 0 0 0 0 1 1 1 1 |
     | 0 0 0 0 0 0 0 1 |
     | 0 0 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 0 |

              8       8
o7 : Matrix ZZ  <-- ZZ
 
i8 : dims(8,C)

o8 = | 1 1 0 0 0 0 0 0 |
     | 0 0 1 1 1 1 1 1 |
     | 0 0 0 0 0 0 1 2 |
     | 0 0 0 0 1 1 1 1 |
     | 0 0 0 0 0 0 0 1 |
     | 0 0 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 0 |

              8       8
o8 : Matrix ZZ  <-- ZZ

See also

Ways to use this method:

The source of this document is in GradedLieAlgebras/doc.m2:1515:0.