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cycles -- make the subalgebra of cycles

Usage:

C=cycles(L)
Inputs:
- L, an instance of the type LieAlgebra,
Outputs:
- C, an instance of the type LieSubAlgebra, the kernel of the differential

Description

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

o1 = L

o1 : LieAlgebra

i2 : D=differentialLieAlgebra({0_L,a})

o2 = D

o2 : LieAlgebra

i3 : C=cycles D

o3 = C

o3 : LieSubAlgebra

i4 : dims(10,C)

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

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

Ways to use cycles:

cycles(LieAlgebra)

For the programmer

The object cycles is a method function.

The source of this document is in GradedLieAlgebras/doc2.m2:1203:0.