M(9,2,16) - Revision history

Charles Eaton at 17:01, 18 December 2018

2018-12-18T17:01:22Z

Charles Eaton at 15:43, 18 December 2018

2018-12-18T15:43:06Z

Charles Eaton at 15:40, 18 December 2018

2018-12-18T15:40:17Z

Charles Eaton: Created page with "{{blockbox |title = M(9,2,16) - $B_0(kPSL_3(4))$ |image = |representative = $B_0(kPSL_3(4))$ |defect = $C_3 \times C_3$ |inertial..."

2018-12-18T15:33:51Z

Created page with "{{blockbox |title = M(9,2,16) - <math>B_0(kPSL_3(4))</math> |image = |representative = <math>B_0(kPSL_3(4))</math> |defect = <math>C_3 \times C_3</math> |inertial..."

New page

{{blockbox
|title = M(9,2,16) - <math>B_0(kPSL_3(4))</math>
|image =
|representative = <math>B_0(kPSL_3(4))</math>
|defect = [[C3xC3|<math>C_3 \times C_3</math>]]
|inertialquotients = <math>Q_8</math>
|k(B) = 6
|l(B) = 5
|k-morita-frob = 1
|Pic-k=
|cartan = <math>\left( \begin{array}{ccccc}
2 & 1 & 1 & 1 & 2 \\
1 & 2 & 1 & 1 & 2 \\
1 & 1 & 2 & 1 & 2 \\
1 & 1 & 1 & 5 & 4 \\
1 & 2 & 2 & 4 & 5 \\
\end{array} \right)</math>
|defect-morita-inv? =
|inertial-morita-inv? =
|O-morita? =
|O-morita =
|decomp = <math>\left( \begin{array}{ccccc}
0 & 0 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 & 1 \\
1 & 0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 & 1 \\
0 & 1 & 0 & 1 & 1 \\
1 & 1 & 1 & 0 & 1 \\
\end{array}\right)</math>
|O-morita-frob = 1
|Pic-O =
|PIgroup =
|source? = No
|sourcereps =
|k-derived-known? = No
|k-derived =
|O-derived-known? = No
|coveringblocks =
|coveredblocks =
|pcoveringblocks =
}}

== Basic algebra ==

'''Quiver:'''

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

== Other notatable representatives ==

<math>B_2(kO'N)</math><ref>See p.202 of [[References|[KKW12]]]</ref>, <math>B_0(kPSL_3(q))</math> for <math>q \equiv 4 \ {\rm or} \ 7 \mod 9</math><ref>See Theorem 1.2 of [[References|[Ku00]]]</ref>

== Projective indecomposable modules ==



== Irreducible characters ==

All irreducible characters have height zero.

[[C3xC3|Back to <math>C_3 \times C_3</math>]]

== Notes ==
<references />

@@ Line 49: / Line 49: @@
 == Other notatable representatives ==
-<math>B_2(kO'N)</math><ref>See p.202 of [[References|[KKW02]]]</ref>, <math>B_0(kPSL_3(q))</math> for <math>q \equiv 4 \ {\rm or} \ 7 \mod 9</math><ref>See Theorem 1.2 of [[References|[Ku00]]]</ref>, <math>B_2(kSuz)</math><ref>See [[References|[KKW04]]]</ref>
+<math>B_2(kO'N)</math><ref>See p.202 of [[References#K|[KKW02]]]</ref>, <math>B_0(kPSL_3(q))</math> for <math>q \equiv 4 \ {\rm or} \ 7 \mod 9</math><ref>See Theorem 1.2 of [[References#K|[Ku00]]]</ref>, <math>B_2(kSuz)</math><ref>See [[References#K|[KKW04]]]</ref>
 == Projective indecomposable modules ==

@@ Line 49: / Line 49: @@
 == Other notatable representatives ==
-<math>B_2(kO'N)</math><ref>See p.202 of [[References|[KKW02]]]</ref>, <math>B_0(kPSL_3(q))</math> for <math>q \equiv 4 \ {\rm or} \ 7 \mod 9</math><ref>See Theorem 1.2 of [[References|[Ku00]]]</ref>
+<math>B_2(kO'N)</math><ref>See p.202 of [[References|[KKW02]]]</ref>, <math>B_0(kPSL_3(q))</math> for <math>q \equiv 4 \ {\rm or} \ 7 \mod 9</math><ref>See Theorem 1.2 of [[References|[Ku00]]]</ref>, <math>B_2(kSuz)</math><ref>See [[References|[KKW04]]]</ref>
 == Projective indecomposable modules ==

M(9,2,16) - Revision history

Charles Eaton at 17:01, 18 December 2018

Charles Eaton at 15:43, 18 December 2018

Charles Eaton at 15:40, 18 December 2018

Charles Eaton: Created page with "{{blockbox |title = M(9,2,16) - B_0(kPSL_3(4)) |image = |representative = B_0(kPSL_3(4)) |defect = C_3 \times C_3 |inertial..."

Charles Eaton: Created page with "{{blockbox |title = M(9,2,16) - $B_0(kPSL_3(4))$ |image = |representative = $B_0(kPSL_3(4))$ |defect = $C_3 \times C_3$ |inertial..."