Input is a permutation of the generators given as a list of cycles. Output is either an error message or the automorphism. The Lie algebra in the exampel below is called the "Opera" case and is taken from the article by Löfwall-Roos cited on the title page.
i1 : L=lieAlgebra({0,1,2,3,4},{[0,0],[0,1],[0,2], {{1,-1},{[1,2],[0,3]}},{{1,2},{[2,2],[1,3]}}, {{1,2},{[2,2],[0,4]}},{{1,-1},{[2,3],[1,4]}},[2,4],[3,4],[4,4]}, genSigns => 1, field => ZZ/5) o1 = L o1 : LieAlgebra |
i2 : symmCyclePermLie {{0,4}} the map is not welldefined |
i3 : symmCyclePermLie {{0,4},{1,3}} o3 = MapLie{...7...} o3 : MapLie |
i4 : peek oo o4 = MapLie{0 => [4] } 1 => [3] 2 => [2] 3 => [1] 4 => [0] sourceLie => L targetLie => L |