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GradedLieAlgebras :: extTableLie

extTableLie -- a table of dimensions of the Ext-algebra of a Lie algebra

Synopsis

Description

This gives a table of dimensions of ExtUL(k,k) where k=L.field. The columns are referring to the degree, indexed from 1, and the rows are referring to the homological degree, also indexed from 1.

i1 : 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})

o1 = L

o1 : LieAlgebra
i2 : L=diffLieAlgebra{L.zz,L.zz,L.zz,b c - a c,a a c - 2 b b b a}

o2 = L

o2 : LieAlgebra
i3 : extTableLie 6

o3 = | 2 1 0 0 0 0 |
     | 0 0 1 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 0 0 |

              6        6
o3 : Matrix ZZ  <--- ZZ

See also

Ways to use extTableLie :