I'm tryng to find all differential homomorphism between $Gl(n, \mathbb{R})$ and $\mathbb{R}$ (viwed as Lie groups). My first thought was find the homomorphis between their the Lie algebras, and then use the relation between the lie groups homomorphism and their Lie algebras. But I find two problems: 1) I don't know how are the homomorphism between $M(n,\mathbb{R})$ and $\mathbb{R}$, and 2) $Gl(n, \mathbb{R})$ is not connected.
So I think that I'm going to the wrong way. Any help wiil b welcome.
Thank You!