Relations in L are elements in ambient(L). When a quotient Lie algebra Q=L/I is constructed, then the elements in the list I must be of type L, but the program converts the relations so that they have type ambient(L) instead. This may be seen by looking at Q.relsLie.
i1 : M = lieAlgebra({a,b,c}) o1 = M o1 : LieAlgebra |
i2 : L = M/{a b} o2 = L o2 : LieAlgebra |
i3 : a c o3 = - (c a) o3 : L |
i4 : Q = L/{a c} o4 = Q o4 : LieAlgebra |
i5 : Q.relsLie o5 = { - (b a), - (c a)} o5 : List |
i6 : oo_1 o6 = - (c a) o6 : M |