Difference between revisions of "C9"

Revision as of 20:18, 5 September 2018

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 mf_\mathcal{O}(B)}[/math]	[math]{\rm mf_k(B)}[/math]
M(9,1,1)	[math]kC_9[/math]	9	1	[math]1[/math]	[math]C_9 : C_6[/math]	1	1
M(9,1,2)	[math]kD_{18}[/math]	6	2	[math]C_2[/math]		1	1
M(9,1,3)	[math]B_0(kPSL_2(8))[/math]	6	2	[math]C_2[/math]		1	1

Blocks in M(9,1,2) are derived equivalent (over [math]\mathcal{O}[/math]) to those in M(9,1,3)

@@ Line 21: / Line 21: @@
 |-
-|<math>M(9,1,1)</math> || <math>kC_9</math> ||9 ||1 ||<math>1</math> ||<math>C_9 : C_6</math> || ||1 ||1 ||
+|[[M(9,1,1)]] || <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 ||
+|[[M(9,1,2)]] || <math>kD_{18}</math> ||6 ||2 || <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 ||
+|[[M(9,1,3)]] || <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>
+Blocks in [[M(9,1,2)]] are derived equivalent (over <math>\mathcal{O}</math>) to those in [[M(9,1,3)]]