When the first argument is an integer, then the dimensions up to that degree are given. When the first argument is a list, then the dimension in that specific multidegree is given. 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 5 o2 = {3, 4, 5, 12, 24} 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 : idealLie(5,{[a,a],d}) o4 = {0, 1, 1, 4, 11} o4 : List |
i5 : idealLie({5,4,0},{[a,a],d}) o5 = 2 |
Below is shown a way to construct the quotient Lie algebra Q=L/I, where I is the ideal generated by [a,a] and d defined above.
i6 : Q=lieAlgebra({a,b,c},{[c,a],[a,a],d},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}}) o6 = Q o6 : LieAlgebra |
i7 : computeLie 5 o7 = {3, 3, 4, 8, 13} o7 : List |