Difference between revisions of "C3"
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| − | |<math>M(3,1,1)</math> || <math>kC_3</math> ||3 ||1 ||<math>1</math> ||<math>S_3</math> || ||1 ||1 || | + | |[[M(3,1,1)|<math>M(3,1,1)</math>]] || <math>kC_3</math> ||3 ||1 ||<math>1</math> ||<math>S_3</math> || ||1 ||1 || |
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| − | |<math>M(3,1,2)</math> || <math>kS_3</math> ||3 ||2 ||<math>C_2</math> ||<math>C_2</math> || ||1 ||1 || | + | |[[M(3,1,2)|<math>M(3,1,2)</math>]] || <math>kS_3</math> ||3 ||2 ||<math>C_2</math> ||<math>C_2</math> || ||1 ||1 || |
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Revision as of 17:00, 28 August 2018
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 |
