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GradedLieAlgebras :: isWellDefined(ZZ,LieDerivation)

isWellDefined(ZZ,LieDerivation) -- whether a Lie derivation is well defined

Synopsis

Description

It is checked that the derivation (d,f): M  → L maps the ideal of relations in M to 0 up to degree n. More precisely, if M=F/I where F is free, and p is the projection F  → M, then the derivation (d*p,f*p): F  → L maps I to 0 in degrees ≤ n. If n is big enough and I is a list, then it is possible to get the information "the derivation is well defined for all degrees".

i1 : F=lieAlgebra{a,b}

o1 = F

o1 : LieAlgebra
i2 : L=F/{a a a b,b b b a}

o2 = L

o2 : LieAlgebra
i3 : e=euler L

o3 = e

o3 : LieDerivation
i4 : isWellDefined(4,e)
the derivation is well defined for all degrees

o4 = true
i5 : d4=lieDerivation{0_L,a b a b a}
warning: the derivation might not be well defined, use isWellDefined

o5 = d4

o5 : LieDerivation
i6 : isWellDefined(4,d4)

o6 = false
i7 : d5=lieDerivation{0_L,b a b a b a}
warning: the derivation might not be well defined, use isWellDefined

o7 = d5

o7 : LieDerivation
i8 : isWellDefined(4,d5)
the derivation is well defined for all degrees

o8 = true
i9 : di=innerDerivation(a b a b a)

o9 = d5

o9 : LieDerivation
i10 : isWellDefined(4,di)
the derivation is well defined for all degrees

o10 = true
i11 : di===d5

o11 = true

See also