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

Synopsis

• Function: isIsomorphism

• Usage:

  b=isIsomorphism(f)

• Inputs:
  • f, an instance of the type LieAlgebraMap, source f == target f
• Outputs:
  • b, a Boolean value, true if $f$ is an isomorphism, false otherwise

Description

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

• trace(ZZ,LieSubSpace,LieAlgebraMap) -- compute the trace of a Lie algebra map acting on a Lie subspace
• isWellDefined(ZZ,LieAlgebraMap) -- whether a Lie map is well defined
• Holonomy Lie algebras and symmetries