- #1

- 2,112

- 18

[tex]

\phi:\mathfrak{g}\to\mathfrak{h}

[/tex]

is a Lie algebra homomorphism, and if [itex]\Phi[/itex] is defined as follows:

[tex]

\Phi:G\to H,\quad \Phi(\exp(A))=\exp(\phi(A))

[/tex]

will [itex]\Phi[/itex] be a group homomorphism?

Since [itex]\exp(A)\exp(B)=\exp(A+B)[/itex] is not true in general, I see no obvious way to prove the claim.