# Difference between revisions of "C4"

## Blocks with defect group $C_4$

These are blocks with cyclic defect groups and so they are described by Brauer trees.

There is a unique $\mathcal{O}$-Morita equivalence class.

Class Representative # lifts / $\mathcal{O}$ $k(B)$ $l(B)$ Inertial quotients ${\rm Pic}_\mathcal{O}(B)$ ${\rm Pic}_k(B)$ ${\rm mf_\mathcal{O}(B)}$ ${\rm mf_k(B)}$ Notes
M(4,1,1) $kC_4$ 1 4 1 $1$ $D_8$ $(k \times k):k^*$ 1 1 45px