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GradedLieAlgebras :: kernelBasisLie

kernelBasisLie -- a basis of the kernel of a Lie homomorphism in a specified degree

Synopsis

Description

Given a Lie homomorphism f, a basis is given for the kernel in the specified degree n (and homological degree d).

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 : kernelBasisLie(5,2,f)

o4 = {[fr , fr , fr ], [fr , fr , fr ], [fr , fr ], [fr , fr ]}
         0    3    3      1    3    3      3    4      3    5

o4 : List
i5 : useLie M

o5 = M

o5 : LieAlgebra
i6 : indexFormLie kernelBasisLie(5,2,f)

o6 = {mb       , mb       , mb       , mb       }
        {5, 32}    {5, 33}    {5, 39}    {5, 41}

o6 : List

See also

Ways to use kernelBasisLie :