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GradedLieAlgebras :: DerLie DerLie

DerLie DerLie -- Lie multiplication of ordinary derivations

Synopsis

Description

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

See also