Difference between revisions of "C9"
(Created page with "== Blocks with defect group <math>C_9</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are three <math>\mathcal{...") |
|||
Line 1: | Line 1: | ||
+ | __NOTITLE__ | ||
+ | |||
== Blocks with defect group <math>C_9</math> == | == Blocks with defect group <math>C_9</math> == | ||
Revision as of 20:05, 5 September 2018
Blocks with defect group [math]C_9[/math]
These are blocks with cyclic defect groups and so they are described by Brauer trees.
There are three [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(9,1,1)[/math] | [math]kC_9[/math] | 9 | 1 | [math]1[/math] | [math]C_9 : C_6[/math] | 1 | 1 | ||
[math]M(9,1,2)[/math] | [math]kD_{18}[/math] | 6 | 2 | [math]C_2[/math] | [math]C_2[/math] | 1 | 1 | ||
[math]M(9,1,3)[/math] | [math]B_0(kPSL_2(8))[/math] | 6 | 2 | [math]C_2[/math] | 1 | 1 |
Blocks in [math]M(9,1,2)[/math] are derived equivalent (over [math]\mathcal{O}[/math]) to those in [math]M(9,1,3)[/math]