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boundaries -- make the subalgebra of boundaries

Usage:

B=boundaries(L)
Inputs:
- L, an instance of the type LieAlgebra,
Outputs:
- B, an instance of the type LieSubAlgebra, the image of the differential

Description

i1 : L=lieAlgebra({a,b},Signs=>{1,0},Weights=>{{2,0},{2,1}},
         LastWeightHomological=>true,Field=>ZZ/3)

o1 = L

o1 : LieAlgebra

i2 : L=differentialLieAlgebra{0_L,a}

o2 = L

o2 : LieAlgebra

i3 : B=boundaries L

o3 = B

o3 : LieSubAlgebra

i4 : dims(10,B)

o4 = | 0 1 0 1 0 0 0 0 0 0 |
     | 0 0 0 0 0 0 0 1 0 1 |
     | 0 0 0 0 0 0 0 1 0 1 |
     | 0 0 0 0 0 0 0 0 0 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 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 |

              10       10
o4 : Matrix ZZ   <-- ZZ

See also

cycles -- make the subalgebra of cycles
lieHomology -- make the homology as a vector space

Ways to use boundaries:

boundaries(LieAlgebra)

For the programmer

The object boundaries is a method function.

The source of this document is in GradedLieAlgebras/doc2.m2:1139:0.