next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: kernelLie

kernelLie -- gives the dimensions of the kernel of a Lie homomorphism up to a specified degree

Synopsis

Description

Given a Lie homomorphism f, the dimensions are given for the kernel up to the specified degree n.

i1 : L=lieAlgebra({a,b,c,r3,r4,r42},
                      {{{1,-1},{[b,c],[a,c]}},[a,b],{{1,-1},{[b,r4],[a,r4]}}},
                      genWeights => {{1,0},{1,0},{2,0},{3,1},{4,1},{4,2}},
                      genDiffs=>{[],[],[],[a,c],[a,a,c],{{1,-1},{[r4],[a,r3]}}},
                      genSigns=>{0,0,0,1,1,0})

o1 = L

o1 : LieAlgebra
i2 : M=minmodelLie 5

o2 = M

o2 : LieAlgebra
i3 : f=M.modelmap

o3 = f

o3 : MapLie
i4 : kernelLie(5,f)

o4 = | 0 1 3 6 14 |
     | 0 1 3 7 18 |
     | 0 0 0 1 4  |
     | 0 0 0 0 0  |
     | 0 0 0 0 0  |

              5        5
o4 : Matrix ZZ  <--- ZZ

See also