M(16,3,3)

M(16,3,3) - [math]k(A_4:C_4)[/math]

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Representative:	[math]k(A_4:C_4)[/math]
Defect groups:	MNA(2,1)
Inertial quotients:	[math]1[/math]
[math]k(B)=[/math]	10
[math]l(B)=[/math]	2
[math]{\rm mf}_k(B)=[/math]	1
[math]{\rm Pic}_k(B)=[/math]
Cartan matrix:	[math]\left( \begin{array}{cc} 8 & 4 \\ 4 & 6 \\ \end{array} \right)[/math]
Defect group Morita invariant?
Inertial quotient Morita invariant?
[math]\mathcal{O}[/math]-Morita classes known?
[math]\mathcal{O}[/math]-Morita classes:
Decomposition matrices:	[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]
[math]{\rm mf}_\mathcal{O}(B)=[/math]
[math]{\rm Pic}_{\mathcal{O}}(B)=[/math]
[math]PI(B)=[/math]
Source algebras known?
Source algebra reps:
[math]k[/math]-derived equiv. classes known?
[math]k[/math]-derived equivalent to:
[math]\mathcal{O}[/math]-derived equiv. classes known?
[math]p'[/math]-index covering blocks:
[math]p'[/math]-index covered blocks:
Index [math]p[/math] covering blocks:

Basic algebra

Quiver: a: <1,2>, b:=<1,1>, c:=<2,1>, d:=<2,2>, e:=<2,2>

Relations w.r.t. [math]k[/math]:

Projective indecomposable modules

Labelling the simple [math]B[/math]-modules by [math]1, 2[/math], the projective indecomposable modules have Loewy structure as follows:

[math]\begin{array}{cc} \begin{array}{c} 1 \\ 1 \ 2 \\ 1 \ 1 \ 2 \\ 1 \ 1 \ 2 \\ 1 \ 2 \\ 1 \\ \end{array}, & \begin{array}{c} 2 \\ 1 \ 2 \ 2 \\ 1 \ 2 \\ 1 \ 2 \\ 1 \\ 2 \\ \end{array} \\ \end{array} [/math]

Irreducible characters

[math]k_0(B)=8[/math], [math]k_1(B)=2[/math]

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