Difference between revisions of "M(9,2,16)"
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== Other notatable representatives == | == Other notatable representatives == | ||
− | <math>B_2(kO'N)</math><ref>See p.202 of [[References|[ | + | <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> |
== Projective indecomposable modules == | == Projective indecomposable modules == |
Revision as of 15:40, 18 December 2018
M(9,2,16) - [math]B_0(kPSL_3(4))[/math]
[[File:|250px]]
Representative: | [math]B_0(kPSL_3(4))[/math] |
---|---|
Defect groups: | [math]C_3 \times C_3[/math] |
Inertial quotients: | [math]Q_8[/math] |
[math]k(B)=[/math] | 6 |
[math]l(B)=[/math] | 5 |
[math]{\rm mf}_k(B)=[/math] | 1 |
[math]{\rm Pic}_k(B)=[/math] | |
Cartan matrix: | [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 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}{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] |
[math]{\rm mf}_\mathcal{O}(B)=[/math] | 1 |
[math]{\rm Pic}_{\mathcal{O}}(B)=[/math] | |
[math]PI(B)=[/math] | |
Source algebras known? | No |
Source algebra reps: | |
[math]k[/math]-derived equiv. classes known? | No |
[math]k[/math]-derived equivalent to: | |
[math]\mathcal{O}[/math]-derived equiv. classes known? | No |
[math]p'[/math]-index covering blocks: | |
[math]p'[/math]-index covered blocks: | |
Index [math]p[/math] covering blocks: |
Contents
Basic algebra
Quiver:
Relations w.r.t. [math]k[/math]:
Other notatable representatives
[math]B_2(kO'N)[/math][1], [math]B_0(kPSL_3(q))[/math] for [math]q \equiv 4 \ {\rm or} \ 7 \mod 9[/math][2]
Projective indecomposable modules
Irreducible characters
All irreducible characters have height zero.
Back to [math]C_3 \times C_3[/math]