C16 - Revision history

Charles Eaton at 10:19, 22 November 2018

2018-11-22T10:19:40Z

Charles Eaton: Categories and Pic_k

2018-10-07T14:19:42Z

Categories and Pic_k

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{16}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

2018-10-04T22:11:18Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_{16}</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

New page

__NOTITLE__

== Blocks with defect group <math>C_{16}</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"| # lifts / <math>\mathcal{O}</math>
! 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

|-
|[[M(16,1,1)]] || <math>kC_{16}</math> || 1 ||16 ||1 ||<math>1</math> ||<math>C_{16}:(C_4 \times C_2)</math> || ||1 ||1 ||
|}

@@ Line 22: / Line 22: @@
 |-
-|[[M(16,1,1)]] || <math>kC_{16}</math> || 1 ||16 ||1 ||<math>1</math> ||<math>C_{16}:(C_4 \times C_2)</math> || ||1 ||1 ||
+|[[M(16,1,1)]] || <math>kC_{16}</math> || 1 ||16 ||1 ||<math>1</math> ||<math>C_{16}:(C_4 \times C_2)</math> || <math>k^{14}:k^*</math> ||1 ||1 ||
 |}

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_{16}</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.

C16 - Revision history

Charles Eaton at 10:19, 22 November 2018

Charles Eaton: Categories and Pic_k

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_{16} == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{16}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There is a uniq..."