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GradedLieAlgebras :: imageLie

imageLie -- gives the dimensions of the image of a Lie homomorphism up to a specified degree

Synopsis

Description

Gives the dimensions of the image of f from degree 1 to n and homological degree from 0 to n-1.

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

o1 = L

o1 : LieAlgebra
i2 : M=minmodelLie 5

o2 = M

o2 : LieAlgebra
i3 : f=M.modelmap

o3 = f

o3 : MapLie
i4 : imageLie(5,f)

o4 = | 2 1 1 1 2 |
     | 0 0 1 2 4 |
     | 0 0 0 0 1 |
     | 0 0 0 0 0 |
     | 0 0 0 0 0 |

              5        5
o4 : Matrix ZZ  <--- ZZ

See also