C27 - Revision history

Charles Eaton at 10:26, 22 November 2018

2018-11-22T10:26:21Z

Charles Eaton at 10:21, 22 November 2018

2018-11-22T10:21:00Z

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{27}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are three..."

2018-09-05T20:14:42Z

Created page with "__NOTITLE__ == Blocks with defect group <math>C_{27}</math> == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are three..."

New page

__NOTITLE__

== Blocks with defect group <math>C_{27}</math> ==

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="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

|-
|[[M(27,1,1)]] || <math>kC_{27}</math> ||27 ||1 ||<math>1</math> ||<math>C_{27} : C_{18}</math> || ||1 ||1 ||
|-
|[[M(27,1,2)]] || <math>kD_{54}</math> ||15 ||2 ||<math>C_2</math> |||| ||1 ||1 ||
|-
|[[M(27,1,3)]] || <math>B_0(kPSL_2(53))</math> ||15 ||2 ||<math>C_2</math> || || ||1 ||1 ||
|}

Blocks in [[M(27,1,2)]] are derived equivalent (over <math>\mathcal{O}</math>) to those in [[M(27,1,3)]].

@@ Line 23: / Line 23: @@
 |[[M(27,1,1)]] || <math>kC_{27}</math> ||27 ||1 ||<math>1</math> ||<math>C_{27} : C_{18}</math> || ||1 ||1 ||
 |-
-|[[M(27,1,2)]] || <math>kD_{54}</math> ||15 ||2 ||<math>C_2</math> |||| ||1 ||1 ||
+|[[M(27,1,2)]] || <math>kD_{54}</math> ||15 ||2 ||<math>C_2</math> || <math>C_{18}</math> || ||1 ||1 ||
 |-
 |[[M(27,1,3)]] || <math>B_0(kPSL_2(53))</math> ||15 ||2 ||<math>C_2</math> || || ||1 ||1 ||

@@ Line 3: / Line 3: @@
 == Blocks with defect group <math>C_{27}</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 are three <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.

C27 - Revision history

Charles Eaton at 10:26, 22 November 2018

Charles Eaton at 10:21, 22 November 2018

Charles Eaton: Created page with "__NOTITLE__ == Blocks with defect group C_{27} == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are three..."

Charles Eaton: Created page with "NOTITLE == Blocks with defect group $C_{27}$ == These are blocks with cyclic defect groups and so they are described by Brauer trees. There are three..."