C8

From Block library
Jump to: navigation, search

Blocks with defect group [math]C_8[/math]

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

There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.

Class Representative # lifts / [math]\mathcal{O}[/math] [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(8,1,1) [math]kC_8[/math] 1 8 1 [math]1[/math] [math]C_8:(C_2 \times C_2)[/math] [math]k^6:k^*[/math] 1 1