C5
Revision as of 09:01, 26 August 2018 by Charles Eaton (talk | contribs) (Created page with "== Blocks with defect group <math>C_5</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are six <math>\mathcal{O}...")
Blocks with defect group [math]C_5[/math]
These are blocks with cyclic defect groups and so they are described by Brauer trees.
There are six [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(5,1,1)[/math] | [math]kC_5[/math] | 5 | 1 | [math]1[/math] | [math]C_5:C_4[/math] | 1 | 1 | ||
| [math]M(5,1,2)[/math] | [math]kD_{10}[/math] | 4 | 2 | [math]C_2[/math] | 1 | 1 | |||
| [math]M(5,1,3)[/math] | [math]B_0(kA_5)[/math] | 4 | 2 | [math]C_2[/math] | 1 | 1 | |||
| [math]M(5,1,4)[/math] | [math]k(C_5:C_4)[/math] | 5 | 4 | [math]C_4[/math] | [math]C_4[/math] | 1 | 1 | ||
| [math]M(5,1,5)[/math] | [math]B_0(kA_7)[/math] | 5 | 4 | [math]C_4[/math] | 1 | 1 | |||
| [math]M(5,1,6)[/math] | faithful block of [math]k(2.A_7)[/math] | 5 | 4 | [math]C_4[/math] | 1 | 1 |
