# M(16,1,1)

M(16,1,1) - $kC_{16}$
Representative: $kC_{16}$ $C_{16}$ $1$ 16 1 1 $k^{14}:k^*$ $\left( \begin{array}{c} 16 \\ \end{array} \right)$ Yes Yes Yes $\mathcal{O} C_{16}$ $\left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right)$ 1 $\mathcal{L}(B)=C_{16}:(C_4 \times C_2)$ {{{PIgroup}}} Yes $kC_{16}$ Yes Forms a derived equivalence class Yes M(16,1,1) M(16,1,1) {{{pcoveringblocks}}}

These are nilpotent blocks.

## Basic algebra

Quiver: a:<1,1>

Relations w.r.t. $k$: $a^{16}=0$

## Projective indecomposable modules

Labelling the unique simple $B$-module by $S_1$, the unique projective indecomposable module has Loewy structure as follows:

$\begin{array}{c} S_1 \\ S_1 \\ \vdots \\ S_1 \\ \end{array}$

## Irreducible characters

All irreducible characters have height zero.