Suppose $A$ is an algebra over a field $k$. I look to the following exercise:
- Show that if $V$ is an irreducible finite dimensional representation of A then any element $z\in Z(A)$ (with $Z(A)$ the center of $A$) acts in V by multiplication by some scalar $\chi_V(z)$ Show that $\chi_V(z)$ is a homomorphism.
I think you have to use the lemma van Schur. I want to construct an intertwining map from $V$ to $V$. Is this the good way? Thank you for hints and solutions :)