The ideal is the least subspace containing the generators of the ideal and which is closed under Lie multiplication by the Lie generators and closed under application of the differential. A basis is given in the specified degree or multi-degree.
i1 : L = lieAlgebra({a,b,c},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}})/{c a} o1 = L o1 : LieAlgebra |
i2 : dimsLie 5 o2 = {3, 4, 5, 12, 24} o2 : List |
i3 : d4=defLie (mb_{4,5}+2*mb_{4,6}) o3 = 2 (b c b a) + (c b b a) o3 : L |
i4 : ib=idealBasisLie(5,{a a,d4}) o4 = {(c c b a a), 2 (c b c b a) + (c c b b a), (c b b a a), (c a b b a), (c ------------------------------------------------------------------------ a b a a), (b c b a a), 2 (b b c b a) + (b c b b a), (b b b a a), (b a b ------------------------------------------------------------------------ a a), (a b b a a), (a a b a a)} o4 : List |
i5 : length oo o5 = 11 |
i6 : indexFormLie ib o6 = {mb , mb + 2mb , mb , mb , mb , mb {5, 7} {5, 13} {5, 15} {5, 5} {5, 9} {5, 2} {5, ------------------------------------------------------------------------ , mb + 2mb , mb , mb , mb , mb } 6} {5, 12} {5, 14} {5, 4} {5, 1} {5, 3} {5, 0} o6 : List |
i7 : idealBasisLie({5,4,0},{a a,d4}) o7 = {(c c b a a), 2 (c b c b a) + (c c b b a)} o7 : List |
i8 : indexFormLie oo o8 = {mb , mb + 2mb } {5, 7} {5, 13} {5, 15} o8 : List |
i9 : F = lieAlgebra({a,b},genWeights=>{{1,0},{2,1}},genSigns=>{1,1},diffl=>true) o9 = F o9 : LieAlgebra |
i10 : Q = diffLieAlgebra{F.zz,a a} o10 = Q o10 : LieAlgebra |
i11 : idealBasisLie(4,{b b}) warning: new generators for the ideal have been added to get invariance of the differential o11 = {(a a b), (b b)} o11 : List |