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GradedLieAlgebras :: kernelTableLie

kernelTableLie -- a table of dimensions of the kernel of a map or derivation

Synopsis

Description

The columns are referring to the degree, indexed from 1, and the rows are referring to the homological degree, indexed from 0.

i1 : L = lieAlgebra({a,b,c,r3,r4,r42},
         genWeights => {{1,0},{1,0},{2,0},{3,1},{4,1},{4,2}},
         genSigns=>{0,0,0,1,1,0},diffl=>true)/{b c - a c,a b,b r4 - a r4}

o1 = L

o1 : LieAlgebra
i2 : L.genDiffs = {L.zz,L.zz,L.zz,a c,a a c,r4 - a r3}

o2 = {0, 0, 0, (b c), (b b c), r4 - (a r3)}

o2 : List
i3 : M = minmodelLie 5

o3 = M

o3 : LieAlgebra
i4 : f = M.modelmap

o4 = f

o4 : MapLie
i5 : kernelTableLie(5,f)

o5 = | 0 1 3 6 14 |
     | 0 1 3 7 17 |
     | 0 0 0 1 4  |
     | 0 0 0 0 1  |
     | 0 0 0 0 0  |

              5        5
o5 : Matrix ZZ  <--- ZZ

See also