C3
Revision as of 12:29, 23 August 2018 by Charles Eaton (talk | contribs) (Created page with "== Blocks with defect group <math>C_3</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are two <math>\mathcal{O}...")
Blocks with defect group [math]C_3[/math]
These are blocks with cyclic defect groups and so they are described by Brauer trees.
There are two [math]\mathcal{O}[/math]-Morita equivalence classes, accounting for all the possible Brauer trees.
| Class | Representative | [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 |
|---|---|---|---|---|---|---|---|---|---|
| [math]M(3,1,1)[/math] | [math]kC_3[/math] | 3 | 1 | [math]1[/math] | [math]S_3[/math] | 1 | 1 | ||
| [math]M(3,1,2)[/math] | [math]kS_3[/math] | 3 | 2 | [math]C_2[/math] | [math]C_2[/math] | 1 | 1 |
