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 |