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

## Synopsis

• Function: isIsomorphism
• Usage:
b=isIsomorphism(f)
• Inputs:
• Outputs:
• b, , true if $f$ is an isomorphism, false otherwise

## 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