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GradedLieAlgebras :: homologyTableLie

homologyTableLie -- a table of dimensions of the homology of a Lie algebra

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 : M=lieAlgebra({a,b,c},genWeights =>
          {{1,0},{1,0},{2,0}},diffl=>true,
          genSigns=>{1,1,0})/{a c-b c, a a c-2 b b b a}

o1 = M

o1 : LieAlgebra
i2 : dimTableLie 7

o2 = | 2 4 3 4 9 17 30 |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |

              7        7
o2 : Matrix ZZ  <--- ZZ
i3 : L=lieAlgebra({a,b,c,r3,r4},genWeights =>
          {{1,0},{1,0},{2,0},{3,1},{4,1}},
          diffl=>true,
          genSigns=>{1,1,0,0,1})

o3 = L

o3 : LieAlgebra
i4 : L=diffLieAlgebra{L.zz,L.zz,L.zz,b c - a c,a a c - 2 b b b a}

o4 = L

o4 : LieAlgebra
i5 : homologyTableLie 7

o5 = | 2 4 3 4 9 17 30 |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |
     | 0 0 0 0 0 0  0  |

              7        7
o5 : Matrix ZZ  <--- ZZ
i6 : Q=L/{b c-a c,a b,b r4-a r4}

o6 = Q

o6 : LieAlgebra
i7 : homologyTableLie 6

o7 = | 2 3 1 0 1 1 |
     | 0 0 1 2 4 7 |
     | 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 |

              6        6
o7 : Matrix ZZ  <--- ZZ

See also

Ways to use homologyTableLie :