### Abstract

We give a general construction which shows that a large class of quantum complete intersections can be realized as the basic algebras of non-principal blocks of finite groups. We investigate the Ext rings of these algebras. We describe how to construct a finite p'-covering for one of these quantum complete intersections, which supports a Hopf algebra structure which is neither commutative nor cocommutative in general. We use this to investigate a problem concerning the definition of nucleus for a non-principal block.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 10 |

Journal | Quarterly Journal of Mathematics |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- quantum groups
- algebras
- varieties
- cohomology
- coverings

## Cite this

Benson, D. J., & Green, E. L. (2004). Non-principal blocks with one simple module.

*Quarterly Journal of Mathematics*,*55*(1), 1-11. https://doi.org/10.1093/qmath/hag039