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GradedLieAlgebras :: subalgBasisLie

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

Synopsis

Description

A basis is given in the specified degree or multidegree. Observe that if the Lie algebra has no differential, then an extra homological degree=0 is added to the given weights of the generators. The function may be used to get a basis for the span of a given set of elements of the same degree, by choosing the degree in input as the degree of the elements.

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 = {{{1, -1}, {[b, c, c, b], [c, b, c, b]}}, {{1, -1}, {[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 = {{{1, -1}, {[b, c, c, b], [c, b, c, b]}}}

o4 : List
i5 : indexFormLie oo

o5 = {- mb        + mb       }
          {4, 17}     {4, 18}

o5 : List
i6 : subalgBasisLie(3,{[a,b,c],[a,c,b],[b,a,c],[b,c,a],[c,b,a],[c,a,b]})

o6 = {[c, b, a], [b, c, a]}

o6 : List

See also

Ways to use subalgBasisLie :