The vector space of graded derivations from L to L with the identity map as defining map, see DerLie, is a graded Lie algebra. If L has a differential δ, then DerLie is a differential graded Lie algebra with differential d->[δ,d]. This Lie algebra is however not of type LieAlgebra, unless a positively graded finite presentation can be given.
i1 : L = lieAlgebra({a,b})/{a a a b,b b b a} o1 = L o1 : LieAlgebra |
i2 : d0 = derLie{a,b} o2 = d0 o2 : DerLie |
i3 : d2 = derLie{a b a,L.zz} o3 = d2 o3 : DerLie |
i4 : d4 = derLie{a b a b a,L.zz} o4 = d4 o4 : DerLie |
i5 : peekLie d2 d4 o5 = a => (a b a b a b a) b => 0 maplie => id sign => 0 weight => {6, 0} sourceLie => L targetLie => L |
i6 : peekLie d0 d4 o6 = a => 4 (a b a b a) b => 0 maplie => id sign => 0 weight => {4, 0} sourceLie => L targetLie => L |