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GradedLieAlgebras :: isIsomorphism(LieAlgebraMap)

isIsomorphism(LieAlgebraMap) -- whether a Lie map is an isomorphism

Synopsis

Description

It is checked that $f$ is surjective and well defined (and commutes with the differential). It follows from this that $f$ is also injective, since the dimensions of source f and target f are equal in each degree.

i1 : L=holonomy{{a0,a1,a2},{a0,a3,a4},{a1,a3,a5},{a2,a4,a5}}

o1 = L

o1 : LieAlgebra
i2 : f=map(L,L,{a5,a2,a4,a1,a3,a0})
warning: the map might not be well defined, 
         use isWellDefined

o2 = f

o2 : LieAlgebraMap
i3 : isIsomorphism f

o3 = true
i4 : g=map(L,L,{a5,a0,a1,a2,a3,a4})
warning: the map might not be well defined, 
         use isWellDefined

o4 = g

o4 : LieAlgebraMap
i5 : isIsomorphism g

o5 = false

See also