Difference between revisions of "C2"
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== Blocks with defect group <math>C_2</math> == | == Blocks with defect group <math>C_2</math> == | ||
| − | These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]]. | + | These are blocks with [[Blocks with cyclic defect groups|cyclic defect groups]] and so they are described by [[Brauer trees]]. |
There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | There is a unique <math>\mathcal{O}</math>-Morita equivalence class. | ||
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! scope="col"| Class | ! scope="col"| Class | ||
! scope="col"| Representative | ! scope="col"| Representative | ||
| + | ! scope="col"| # lifts / <math>\mathcal{O}</math> | ||
! scope="col"| <math>k(B)</math> | ! scope="col"| <math>k(B)</math> | ||
! scope="col"| <math>l(B)</math> | ! scope="col"| <math>l(B)</math> | ||
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|- | |- | ||
| − | |[[M(2,1,1)]] || <math>kC_2</math> ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k</math> ||1 ||1 || | + | |[[M(2,1,1)]] || <math>kC_2</math> || 1 ||2 ||1 ||<math>1</math> ||<math>C_2</math> ||<math>k^*</math> ||1 ||1 || |
|} | |} | ||
[[Category:Cyclic p-group]] | [[Category:Cyclic p-group]] | ||
[[Category: p-group]] | [[Category: p-group]] | ||
Latest revision as of 21:59, 21 November 2018
Blocks with defect group [math]C_2[/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(2,1,1) | [math]kC_2[/math] | 1 | 2 | 1 | [math]1[/math] | [math]C_2[/math] | [math]k^*[/math] | 1 | 1 |
