C8 - Revision history

Charles Eaton at 10:19, 22 November 2018

2018-11-22T10:19:03Z

Charles Eaton: Categories and Pic_k

2018-10-07T14:12:54Z

Categories and Pic_k

Charles Eaton: Added lifting column

2018-09-15T08:06:08Z

Added lifting column

Charles Eaton at 14:43, 8 September 2018

2018-09-08T14:43:06Z

Charles Eaton: /* Blocks with defect group C_8 */

2018-08-26T21:22:56Z

‎Blocks with defect group C_8

Charles Eaton at 21:22, 26 August 2018

2018-08-26T21:22:34Z

Charles Eaton: Created page with "== Blocks with defect group $C_8$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a unique $\mathca..."$

2018-08-26T21:18:55Z

Created page with "== Blocks with defect group <math>C_8</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a unique <math>\mathca..."

New page

== Blocks with defect group <math>C_8</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="wikitable"
|-
! scope="col"| Class
! scope="col"| Representative
! scope="col"| <math>k(B)</math>
! scope="col"| <math>l(B)</math>
! scope="col"| Inertial quotients
! scope="col"| <math>{\rm Pic}_\mathcal{O}(B)</math>
! scope="col"| <math>{\rm Pic}_k(B)</math>
! scope="col"| <math>{\rm mf_\mathcal{O}(B)}</math>
! scope="col"| <math>{\rm mf_k(B)}</math>
! scope="col"| Notes

|-
|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:C_4</math> || ||1 ||1 ||
|}

@@ Line 22: / Line 22: @@
 |-
-|[[M(8,1,1)]] || <math>kC_8</math> || 1 ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(8,1,1)]] || <math>kC_8</math> || 1 ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || <math>k^6:k^*</math> ||1 ||1 ||
 |}

@@ Line 1: / Line 1: @@
 == Blocks with defect group <math>C_8</math> ==
@@ Line 19: / Line 21: @@
 |-
-|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(8,1,1)]] || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
 |}

@@ Line 19: / Line 19: @@
 |-
-|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C2)</math> || ||1 ||1 ||
+|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
 |}

@@ Line 19: / Line 19: @@
 |-
-|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:C_4</math> || ||1 ||1 ||
+|<math>M(8,1,1)</math> || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C2)</math> || ||1 ||1 ||
 |}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_8</math> ==
-These are blocks with [[cyclic defect groups]] and so they are described by [[Brauer trees]].
+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.

@@ Line 11: / Line 11: @@
 ! scope="col"| Class
 ! scope="col"| Representative
 ! scope="col"| <math>k(B)</math>
 ! scope="col"| <math>l(B)</math>
@@ Line 21: / Line 22: @@
 |-
-|[[M(8,1,1)]] || <math>kC_8</math> ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
+|[[M(8,1,1)]] || <math>kC_8</math> || 1 ||8 ||1 ||<math>1</math> ||<math>C_8:(C_2 \times C_2)</math> || ||1 ||1 ||
 |}