The permutation x of the generators is given as a list of cycles. The subspace of L in degree d, generated by the elements in y, should be invariant under x and the output characterLie(d,x,y) gives the trace of x as 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(3,{{a,b,c}}, basisLie(3)) o3 = -1 ZZ o3 : -- 31 |
i4 : permopLie({{a,b,c}},[c,b,a]) o4 = {{1, -1}, {[b, c, a], [c, b, a]}} o4 : List |
i5 : permopLie({{a,b,c}},[b,c,a]) o5 = {{-1}, {[c, b, a]}} o5 : List |