A derivation d:M->L has a weight which is the difference between the weight of any non-zero output and a non-zero input. The weight of the zero derivation is defined as {0,...,0} with as many zeroes as the length of weightLie(x) for any x in M or L. The weight is obtained as d.weight and may be seen using peekLie d.
i1 : L=lieAlgebra{a,b}/{a a a b,b b b a} o1 = L o1 : LieAlgebra |
i2 : M=lieAlgebra({a1,b1},genWeights=>{3,3}) o2 = M o2 : LieAlgebra |
i3 : useLie L o3 = L o3 : LieAlgebra |
i4 : f=mapLie(L,M,{a a b,b b a}) o4 = f o4 : MapLie |
i5 : d=derLie(f,{a,b}) o5 = d o5 : DerLie |
i6 : peekLie d o6 = a1 => a b1 => b maplie => MapLie{a1 => - (a b a)} b1 => (b b a) sourceLie => M targetLie => L sign => 0 weight => {-2, 0} sourceLie => M targetLie => L |
i7 : d.weight o7 = {-2, 0} o7 : List |