M(16,3,2) - Revision history

Charles Eaton at 09:51, 15 August 2019

2019-08-15T09:51:27Z

Charles Eaton: /* Irreducible characters */

2019-08-14T17:05:34Z

‎Irreducible characters

Charles Eaton: Quiver

2019-08-14T16:11:16Z

Quiver

Charles Eaton: Created page with "{{blockbox |title = M(16,3,2) - $k(SmallGroup(48,30))$ |image = |representative = $k(SmallGroup(48,30))$ |defect = MNA(2,1) |inertialquotients = <..."

2018-11-24T09:31:44Z

Created page with "{{blockbox |title = M(16,3,2) - <math>k(SmallGroup(48,30))</math> |image = |representative = <math>k(SmallGroup(48,30))</math> |defect = MNA(2,1) |inertialquotients = <..."

New page

{{blockbox
|title = M(16,3,2) - <math>k(SmallGroup(48,30))</math>
|image =
|representative = <math>k(SmallGroup(48,30))</math>
|defect = [[MNA(2,1)]]
|inertialquotients = <math>1</math>
|k(B) = 10
|l(B) = 2
|k-morita-frob = 1
|Pic-k=
|cartan = <math>\left( \begin{array}{cc}
8 & 4 \\
4 & 6 \\
\end{array} \right)</math>
|defect-morita-inv? =
|inertial-morita-inv? =
|O-morita? =
|O-morita =
|decomp = <math>\left( \begin{array}{cc}
1 & 0 \\
1 & 0 \\
1 & 0 \\
1 & 0 \\
0 & 1 \\
0 & 1 \\
1 & 1 \\
1 & 1 \\
1 & 1 \\
1 & 1 \\
\end{array}\right)</math><ref>This is the only possible decomposition matrix with the given Cartan matrix.</ref>
|O-morita-frob =
|Pic-O =
|PIgroup =
|source? =
|sourcereps =
|k-derived-known? =
|k-derived =
|O-derived-known? =
|coveringblocks =
|coveredblocks =
|pcoveringblocks =
}}

== Basic algebra ==

'''Quiver:'''

'''Relations w.r.t. <math>k</math>:'''

== Other notatable representatives ==

== Projective indecomposable modules ==

== Irreducible characters ==

<math>k_0(B)=8</math>, <math>k_1(b)=2</math>

[[MNA(2,1)|Back to <math>MNA(2,1)</math>]]

== Notes ==
<references />

@@ Line 1: / Line 1: @@
 {{blockbox
-|title = M(16,3,2) - <math>k(SmallGroup(48,30))</math>
+|title = M(16,3,2) - <math>B_0(k(A_5:C_4))</math>
 |image =
-|representative =  <math>k(SmallGroup(48,30))</math>
+|representative =  <math>B_0(k(A_5:C_4))</math>
 |defect = [[MNA(2,1)]]
 |inertialquotients = <math>1</math>
@@ Line 10: / Line 10: @@
 |Pic-k=
 |cartan = <math>\left( \begin{array}{cc}
-& 4 \\
+& 8 \\
 & 6 \\
 \end{array} \right)</math>
 |defect-morita-inv? =
@@ Line 22: / Line 22: @@
 & 0 \\
 & 0 \\
 & 1 \\
 & 1 \\
 & 1 \\
 & 1 \\
 & 1 \\
 & 1 \\
-\end{array}\right)</math><ref>This is the only possible decomposition matrix with the given Cartan matrix.</ref>
+\end{array}\right)</math>
 |O-morita-frob =
 |Pic-O =
@@ Line 44: / Line 44: @@
 == Basic algebra ==
-'''Quiver:''' a: <1,2>, b:=<1,1>, c:=<2,1>, d:=<2,2>, e:=<2,2>
+'''Quiver:'''
 '''Relations w.r.t. <math>k</math>:'''

@@ Line 54: / Line 54: @@
 == Irreducible characters ==
-<math>k_0(B)=8</math>, <math>k_1(b)=2</math>
+<math>k_0(B)=8</math>, <math>k_1(B)=2</math>
 [[MNA(2,1)|Back to <math>MNA(2,1)</math>]]

M(16,3,2) - Revision history

Charles Eaton at 09:51, 15 August 2019

Charles Eaton: /* Irreducible characters */

Charles Eaton: Quiver

Charles Eaton: Created page with "{{blockbox |title = M(16,3,2) - k(SmallGroup(48,30)) |image = |representative = k(SmallGroup(48,30)) |defect = MNA(2,1) |inertialquotients = <..."

Charles Eaton: Created page with "{{blockbox |title = M(16,3,2) - $k(SmallGroup(48,30))$ |image = |representative = $k(SmallGroup(48,30))$ |defect = MNA(2,1) |inertialquotients = <..."