Let $\mathcal{U}_q$ be the set of endomorphisms $\phi \in \mathcal{L}(V)$ that are compatible with $P_a$. Show that $\mathcal{U}_q$ is a subalgebra of $\mathcal{L}(V)$.
Let $\mathcal{U}_q$ be the set of endomorphisms $\phi \in \mathcal{L}(V)$ that are compatible with $P_a$. Show that $\mathcal{U}_q$ is a subalgebra of $\mathcal{L}(V)$.