Four-subspace quiver ($S_4$)

The four-subspace quiver has four sources with arrows into one sink. Four one-dimensional sources mapped to the lines $k{e}_1$, $k{e}_2$, $k(e_1+e_2)$ and $k(\lambda e_1+e_2)$ in $k^2$ give a brick module for every $\lambda$. Preserving the first three lines forces scalar endomorphisms. Its Tits form of a quiver is zero, so the Ringel form gives one-dimensional self-extensions.