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 |