Below is an example of a periodic Lie algebra (a periodization of sl3) with random quadratic relations.
i1 : rels=apply(7,i->randomLie(2,{a,b,c,d,e}, field => ZZ/7)) o1 = {{{3, 0, 1, 3, 0, 2, 3, -3, 3, 3}, {[b, a], [c, a], [d, a], [e, a], [c, ------------------------------------------------------------------------ b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{0, -2, 0, -2, 3, -2, 0, ------------------------------------------------------------------------ -2, 2, 3}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, ------------------------------------------------------------------------ c], [e, c], [e, d]}}, {{-1, -1, 3, -1, 0, 2, -1, 1, 3, -1}, {[b, a], [c, ------------------------------------------------------------------------ a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, ------------------------------------------------------------------------ {{1, -1, 2, -1, 0, 2, -1, 1, -2, -1}, {[b, a], [c, a], [d, a], [e, a], ------------------------------------------------------------------------ [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}, {{3, -2, -1, 3, -2, ------------------------------------------------------------------------ -1, 1, 3, -3, 2}, {[b, a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, ------------------------------------------------------------------------ b], [d, c], [e, c], [e, d]}}, {{-2, 0, -1, -3, 3, 3, 1, 0, 3, -1}, {[b, ------------------------------------------------------------------------ a], [c, a], [d, a], [e, a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, ------------------------------------------------------------------------ d]}}, {{1, 1, 2, 2, 1, -1, -1, -1, -1, 2}, {[b, a], [c, a], [d, a], [e, ------------------------------------------------------------------------ a], [c, b], [d, b], [e, b], [d, c], [e, c], [e, d]}}} o1 : List |
i2 : L = lieAlgebra({a,b,c,d,e}, rels, field=>ZZ/7) o2 = L o2 : LieAlgebra |
i3 : computeLie 8 o3 = {5, 3, 5, 3, 5, 3, 5, 3} o3 : List |
i4 : randomLie({4,0}) o4 = {{-2, -1, -3}, {[d, e, e, a], [e, e, e, a], [e, e, e, d]}} o4 : List |