Indecomposable modules for a cyclic p-group ($V_i=k[t]/(t^i)$)

For $P$ cyclic of order $q=p^n$ in characteristic $p$, its group algebra is $k[t]/(t^q)$. The nilpotent Jordan normal form classifies its indecomposable finite-dimensional modules as $V_i$, $1\le i\le q$. A module homomorphism $V_i\to V_j$ is determined by an element annihilated by $t^i$, so its dimension is $\min (i,j)$.