A basis is given in the specified degree or multidegree. Observe that if the Lie algebra has no differential, then an extra homological degree=0 is added to the given weights of the generators.
i1 : L = lieAlgebra({a,b,c},{[c,a]},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}}) o1 = L o1 : LieAlgebra |
i2 : computeLie 4 o2 = {3, 4, 5, 12} o2 : List |
i3 : d=defLie (mb_{4,5}+2*mb_{4,6}) o3 = {{1, 2}, {[c, b, b, a], [b, c, b, a]}} o3 : List |
i4 : i=idealBasisLie(5,{[a,a],d}) o4 = {[c, c, b, a, a], {{2, 1}, {[c, b, c, b, a], [c, c, b, b, a]}}, [c, b, ------------------------------------------------------------------------ b, a, a], [c, a, b, b, a], [c, a, b, a, a], [b, c, b, a, a], {{2, 1}, ------------------------------------------------------------------------ {[b, b, c, b, a], [b, c, b, b, a]}}, [b, b, b, a, a], [b, a, b, a, a], ------------------------------------------------------------------------ [a, b, b, a, a], [a, a, b, a, a]} o4 : List |
i5 : length oo o5 = 11 |
i6 : idealLie(5,{[a,a],d}) o6 = {0, 1, 1, 4, 11} o6 : List |
i7 : weightLie i o7 = {{5, 4, 0}, {5, 4, 0}, {5, 2, 0}, {5, 2, 0}, {5, 2, 0}, {5, 2, 0}, {5, ------------------------------------------------------------------------ 2, 0}, {5, 0, 0}, {5, 0, 0}, {5, 0, 0}, {5, 0, 0}} o7 : List |
i8 : idealBasisLie({5,4,0},{[a,a],d}) o8 = {[c, c, b, a, a], {{2, 1}, {[c, b, c, b, a], [c, c, b, b, a]}}} o8 : List |
i9 : indexFormLie oo o9 = {mb , mb + 2mb } {5, 7} {5, 13} {5, 15} o9 : List |
i10 : indexFormLie i o10 = {mb , mb + 2mb , mb , mb , mb , mb {5, 7} {5, 13} {5, 15} {5, 5} {5, 9} {5, 2} {5, ----------------------------------------------------------------------- , mb + 2mb , mb , mb , mb , mb } 6} {5, 12} {5, 14} {5, 4} {5, 1} {5, 3} {5, 0} o10 : List |