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GradedLieAlgebras :: imageBasisLie

imageBasisLie -- a basis of the image of a Lie homomorphism or derivation in a specified degree

Synopsis

Description

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 : peekLie f

o5 = MapLie{fr_0 => a                   }
            fr_1 => b
            fr_2 => c
            fr_3 => 0
            fr_4 => r3
            fr_5 => r3
            fr_6 =>  - (a r42) + (b r42)
            sourceLie => M
            targetLie => L
i6 : imageTableLie(5,f)

o6 = | 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
o6 : Matrix ZZ  <--- ZZ
i7 : imageBasisLie(5,f)

o7 = {(b b b c), (b b r3), (b a r3), (a a r3), (a r42) - (b r42), (c b c), (c
     ------------------------------------------------------------------------
     r3)}

o7 : List
i8 : imageBasisLie(5,1,f)

o8 = {(b b r3), (b a r3), (a a r3), (c r3)}

o8 : List
i9 : d = diffLie()

o9 = d

o9 : DerLie
i10 : imageBasisLie(5,1,d)

o10 = {(b r4) - (b a r3), (a a r3) - (b a r3)}

o10 : List
i11 : boundariesBasisLie(5,1)

o11 = {(b r4) - (b a r3), (a a r3) - (b a r3)}

o11 : List

See also

Ways to use imageBasisLie :