Four-subspace quiver
= Four-subspace quiver
{title2=$S_4$}
The <four-subspace quiver> has four sources with arrows into one sink. Four one-dimensional sources mapped to the lines $ke_1$, $ke_2$, $k(e_1+e_2)$ 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.