# M(16,10,1)

Revision as of 09:41, 4 December 2018 by Charles Eaton (talk | contribs) (Created page with "{{blockbox |title = M(16,10,1) - <math>k(C_4 \times C_2 \times C_2)</math> |image = |representative = <math>k(C_4 \times C_2 \times C_2)</math> |defect = <math>C_4 \times C...")

M(16,10,1) - [math]k(C_4 \times C_2 \times C_2)[/math]

[[File:|250px]]

Representative: | [math]k(C_4 \times C_2 \times C_2)[/math] |
---|---|

Defect groups: | [math]C_4 \times C_2 \times C_2[/math] |

Inertial quotients: | [math]1[/math] |

[math]k(B)=[/math] | 16 |

[math]l(B)=[/math] | 1 |

[math]{\rm mf}_k(B)=[/math] | 1 |

[math]{\rm Pic}_k(B)=[/math] | |

Cartan matrix: | [math]\left( \begin{array}{c} 16 \\ \end{array} \right)[/math] |

Defect group Morita invariant? | Yes |

Inertial quotient Morita invariant? | Yes |

[math]\mathcal{O}[/math]-Morita classes known? | Yes |

[math]\mathcal{O}[/math]-Morita classes: | [math]\mathcal{O} (C_4 \times C_2 \times C_2)[/math] |

Decomposition matrices: | [math]\left( \begin{array}{c} 1 \\ 1 \\ \vdots \\ 1 \\ \end{array}\right)[/math] |

[math]{\rm mf}_\mathcal{O}(B)=[/math] | 1 |

[math]{\rm Pic}_{\mathcal{O}}(B)=[/math] | [math]\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)[/math] |

[math]PI(B)=[/math] | |

Source algebras known? | No |

Source algebra reps: | |

[math]k[/math]-derived equiv. classes known? | Yes |

[math]k[/math]-derived equivalent to: | Forms a derived equivalence class |

[math]\mathcal{O}[/math]-derived equiv. classes known? | Yes |

[math]p'[/math]-index covering blocks: | M(16,10,1), M(16,10,3) (complete) |

[math]p'[/math]-index covered blocks: | M(16,10,1), M(16,10,3)^{[1]} (complete) |

Index [math]p[/math] covering blocks: |

These are nilpotent blocks.

## Basic algebra

**Quiver:** a:<1,1>, b:<1,1>, c:<1,1>

**Relations w.r.t. [math]k[/math]:** [math]a^4=b^2=c^2=0[/math], [math]ab+ba=ac+ca=bc+cb=0[/math]

## Projective indecomposable modules

## Irreducible characters

All irreducible characters have height zero.

Back to [math]C_4 \times C_2 \times C_2[/math]