Difference between revisions of "C3"

From Block library
Jump to: navigation, search
(Blocks with defect group C_3)
Line 21: Line 21:
  
 
|-
 
|-
|[[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 ||  
+
|[[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 || [[Image:M(3,1,1)tree.png|45px]]
 
|-
 
|-
|[[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 ||  
+
|[[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 || [[Image:M(3,1,2)tree.png|45px]]
 
|}
 
|}

Revision as of 12:27, 9 September 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 M(3,1,1)tree.png
[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)tree.png