The permutation x of the generators is given as a list of cycles, the identity is written {{}}. The permutation should define an automorphism on L. The subspace of L in degree d, generated by the elements in y, should be invariant under x and the output characterLie(x,y) gives the trace of x, which is an element in L.field.
i1 : L = lieAlgebra({a,b,c}, field=>ZZ/31) o1 = L o1 : LieAlgebra |
i2 : basisLie 3 o2 = {(a b a), (b b a), (c b a), (a c a), (b c a), (c c a), (b c b), (c c b)} o2 : List |
i3 : characterLie({{a,b,c}}, basisLie(3)) o3 = -1 ZZ o3 : -- 31 |
i4 : permopLie({{a,b,c}},c b a) o4 = (b c a) - (c b a) o4 : L |
i5 : permopLie({{a,b,c}},b c a) o5 = - (c b a) o5 : L |