# M(8,2,1)

M(8,2,1) - $k(C_4 \times C_2)$
Representative: $k(C_4 \times C_2)$ $C_4 \times C_2$ $1$ 8 1 1 $\left( \begin{array}{c} 8 \\ \end{array} \right)$ Yes Yes Yes $\mathcal{O} (C_4 \times C_2)$ $\left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right)$ 1 $(C_4 \times C_2):(C_2 \times C_2 \times C_2)$ Yes Forms a derived equivalence class Yes M(8,2,1) M(8,2,1) M(16,2,1), M(16,3,1), M(16,4,1), M(16,11,1), M(16,12,1), M(16,13,1)

These are nilpotent blocks.

## Basic algebra

Quiver: a:<1,1>, b:<1,1>

Relations w.r.t. $k$: a^4=b^2=ab+ba=0

## Projective indecomposable modules

Labelling the unique simple $B$-module by $1$, the unique projective indecomposable module has Loewy structure as follows:

$\begin{array}{c} 1 \\ 1 \ 1 \\ 1 \ 1 \\ 1 \ 1 \\ 1 \\ \end{array}$

## Irreducible characters

All irreducible characters have height zero.