M(5,1,3) - Revision history

Charles Eaton: Added image

2018-09-04T09:31:10Z

Added image

2018-09-02T21:59:47Z

2018-09-02T21:57:38Z

2018-09-02T21:16:39Z

2018-09-02T19:55:54Z

@@ Line 44: / Line 44: @@
 Let <math>N \triangleleft G</math> with <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.
-If <math>b</math> lies in M(5,1,3), then <math>B</math> must lie in M(5,1,3) or [[M(5,1,5)]].
+If <math>b</math> lies in M(5,1,3), then <math>B</math> must lie in M(5,1,3) or [[M(5,1,5)]]. <span style="color: red">Examples needed.</span>
 <!-- If <math>B</math> lies in M(5,1,3), then <math>b</math> must lie in [[M(5,1,1)]], M(5,1,2) or [[M(5,1,4)]]. <span style="color: red">Examples needed.</span>

@@ Line 1: / Line 1: @@
 {{blockbox
 |title = M(5,1,3) - <math>B_0(kA_5)</math>
-|image =
+|image = M(5,1,3)quiver.png
 |representative =  <math>B_0(kA_5)</math>
 |defect = [[C5|<math>C_5</math>]]

@@ Line 42: / Line 42: @@
 == Covering blocks and covered blocks ==
-<!--   Let <math>N \triangleleft G</math> with <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.
+Let <math>N \triangleleft G</math> with <math>p'</math>-index and let <math>B</math> be a block of <math>\mathcal{O} G</math> covering a block <math>b</math> of <math>\mathcal{O} N</math>.
-If <math>b</math> lies in M(5,1,2), then <math>B</math> must lie in [[M(5,1,1)]], M(5,1,2) or [[M(5,1,4)]].
+If <math>b</math> lies in M(5,1,3), then <math>B</math> must lie in M(5,1,3) or [[M(5,1,5)]].
-If <math>B</math> lies in M(5,1,2), then <math>b</math> must lie in [[M(5,1,1)]], M(5,1,2) or [[M(5,1,4)]]. <span style="color: red">Examples needed.</span>
+<!-- If <math>B</math> lies in M(5,1,3), then <math>b</math> must lie in [[M(5,1,1)]], M(5,1,2) or [[M(5,1,4)]]. <span style="color: red">Examples needed.</span>
   -->

@@ Line 34: / Line 34: @@
 == Basic algebra ==
-'''Quiver:'''
+'''Quiver:''' a:<1,2>, b:<2,1>, c:<2,2>
-'''Relations w.r.t. <math>k</math>:'''
+'''Relations w.r.t. <math>k</math>:''' ac=cb=ba-c^2=0
 == Other notatable representatives ==
@@ Line 47: / Line 47: @@
 If <math>B</math> lies in M(5,1,2), then <math>b</math> must lie in [[M(5,1,1)]], M(5,1,2) or [[M(5,1,4)]]. <span style="color: red">Examples needed.</span>
 == Projective indecomposable modules ==
@@ Line 54: / Line 56: @@
 <math>\begin{array}{cc}
     \begin{array}{c}
        S_1 \\
        S_2 \\
        S_1 \\
     \end{array}, &
-\begin{array}{c}
+\begin{array}{ccc}
-      S_2 \\
+     & S_2 & \\
-       S_1 \\
+       S_1 & & S_2 \\
-      S_2 \\
+     & S_2 & \\
 \end{array}
 \end{array}
 </math>
-           -->
 == Irreducible characters ==
 All irreducible characters have height zero.