The vector space D of graded derivations from L to L with the identity map as defining map, see LieDerivation, is a graded Lie algebra. If L has a differential del, then D is a differential graded Lie algebra with differential d → [del,d].
i1 : L = lieAlgebra{a,b}/{a a a b,b b b a} o1 = L o1 : LieAlgebra |
i2 : d0 = lieDerivation{a,b} o2 = d0 o2 : LieDerivation |
i3 : d2 = lieDerivation{a b a,0_L} warning: the derivation might not be well defined, use isWellDefined o3 = d2 o3 : LieDerivation |
i4 : d4 = lieDerivation{a b a b a,0_L} warning: the derivation might not be well defined, use isWellDefined o4 = d4 o4 : LieDerivation |
i5 : describe d2 d4 o5 = a => (a b a b a b a) b => 0 map => id_L sign => 0 weight => {6, 0} source => L target => L |
i6 : describe d0 d4 o6 = a => 4 (a b a b a) b => 0 map => id_L sign => 0 weight => {4, 0} source => L target => L |