Charles Eaton: Created page with "{{blockbox |title = M(16,10,2) - $B_0(k(C_4 \times A_5))$ |image = M(8,5,2)quiver.png |representative = $B_0(k(C_4 \times A_5))$ |defect = C4xC2xC2|<..."

2018-12-05T08:31:55Z

Created page with "{{blockbox |title = M(16,10,2) - <math>B_0(k(C_4 \times A_5))</math> |image = M(8,5,2)quiver.png |representative = <math>B_0(k(C_4 \times A_5))</math> |defect = C4xC2xC2|<..."

New page

{{blockbox
|title = M(16,10,2) - <math>B_0(k(C_4 \times A_5))</math>
|image = M(8,5,2)quiver.png
|representative = <math>B_0(k(C_4 \times A_5))</math>
|defect = [[C4xC2xC2|<math>C_4 \times C_2 \times C_2</math>]]
|inertialquotients = <math>C_3</math>
|k(B) = 16
|l(B) = 3
|k-morita-frob = 1
|Pic-k=
|cartan = <math>\left( \begin{array}{ccc}
8 & 8 & 4 \\
8 & 16 & 8 \\
4 & 8 & 8 \\
\end{array} \right)</math>
|defect-morita-inv? = Yes
|inertial-morita-inv? = Yes
|O-morita? = Yes
|O-morita = <math>B_0(\mathcal{O}(C_4\times A_5))</math>
|decomp = <math>\left( \begin{array}{ccc}
0 & 1 & 0 \\
0 & 1 & 0 \\
0 & 1 & 0 \\
0 & 1 & 0 \\
1 & 1 & 0 \\
1 & 1 & 0 \\
1 & 1 & 0 \\
1 & 1 & 0 \\
0 & 1 & 1 \\
0 & 1 & 1 \\
0 & 1 & 1 \\
0 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1 \\
\end{array}\right)</math>
|O-morita-frob = 1
|Pic-O = <math>D_8 \times C_2</math><ref><math>{\rm Pic}_{\mathcal{O}}(B_0(\mathcal{O}(C_4 \times A_5)))=\mathcal{L}(B_0(\mathcal{O}(C_4 \times A_5)))=\mathcal{L}(\mathcal{O}C_4) \times \mathcal{T}(B_0(\mathcal{O}A_5))</math> by [[References|[EL18c]]], giving the isomorphism type of <math>{\rm Pic}_\mathcal{O}(B)</math> in general.</ref>
|PIgroup = <math>D_8 \times S_4 \times C_2</math><ref>By Theorem 3.7 of [[References|[EL18c]]].</ref>
|source? = No
|sourcereps =
|k-derived-known? = Yes
|k-derived = [[M(16,10,3)]]
|O-derived-known? = Yes
|coveringblocks =
|coveredblocks =
|pcoveringblocks =
}}

== Basic algebra ==

'''Quiver:''' a:<1,2>, b:<2,3>, c:<3,2>, d:<2,1>, e:<1,1>, f: <2,2>, g:<3,3>

'''Relations w.r.t. <math>k</math>:''' <math>ad=cb=0</math>, <math>bcda=dabc</math>, <math>e^4=f^4=g^4=0</math>, <math>af=ea</math>, <math>bg=fb</math>, <math>cf=gc</math>, <math>de=fd</math>

== Other notatable representatives ==

== Projective indecomposable modules ==

== Irreducible characters ==

All irreducible characters have height zero.

[[C4xC2xC2|Back to <math>C_4 \times C_2 \times C_2</math>]]

== Notes ==

<references />

[[Category: Morita equivalence classes|16,10,2]]
[[Category: Blocks with defect group C4xC2xC2]]

M(16,10,2) - Revision history

Charles Eaton: Created page with "{{blockbox |title = M(16,10,2) - B_0(k(C_4 \times A_5)) |image = M(8,5,2)quiver.png |representative = B_0(k(C_4 \times A_5)) |defect = C4xC2xC2|<..."

Charles Eaton: Created page with "{{blockbox |title = M(16,10,2) - $B_0(k(C_4 \times A_5))$ |image = M(8,5,2)quiver.png |representative = $B_0(k(C_4 \times A_5))$ |defect = C4xC2xC2|<..."