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GradedLieAlgebras :: subalgBasisLie

subalgBasisLie -- computes a basis of a Lie subalgebra in a given degree or multi-degree

Synopsis

Description

A basis is given in the specified degree or multi-degree. The subalgebra is the least subspace containing the generators in genlist and which is closed under Lie multiplication and the differential. If the degree n is the same as the degree of the elements in the list genlist, one obtains a method to compute a basis for the subspace in degree n generated by genlist (and the differential).

i1 : L = lieAlgebra({a,b,c},genSigns=>{1,0,1},genWeights=>{{1,0},{1,2},{1,0}})

o1 = L

o1 : LieAlgebra
i2 : subalgBasisLie(4,{a,b c})

o2 = {(b c c b) - (c b c b), (b c a a) - (c b a a)}

o2 : List
i3 : indexFormLie oo

o3 = {- mb        + mb       , - mb       + mb      }
          {4, 17}     {4, 18}      {4, 2}     {4, 4}

o3 : List
i4 : subalgBasisLie({4,4,0},{a,b c})

o4 = {(b c c b) - (c b c b)}

o4 : List
i5 : subalgBasisLie(3,{a b c,a c b,b a c,b c a,c b a,c a b})

o5 = {(c b a), (b c a)}

o5 : List
i6 : F = lieAlgebra({a,b},genWeights=>{{2,0},{2,1}},genSigns=>{1,0},diffl=>true)

o6 = F

o6 : LieAlgebra
i7 : Q = diffLieAlgebra{F.zz,a}

o7 = Q

o7 : LieAlgebra
i8 : subalgBasisLie(2,{b})

o8 = {b, a}

o8 : List

See also

Ways to use subalgBasisLie :