### 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 |
---|---|

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

*Quarterly Journal of Mathematics*,

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

**Non-principal blocks with one simple module.** / Benson, David John; Green, Edward L. .

Research output: Contribution to journal › Article

*Quarterly Journal of Mathematics*, vol. 55, no. 1, pp. 1-11. https://doi.org/10.1093/qmath/hag039

}

TY - JOUR

T1 - Non-principal blocks with one simple module

AU - Benson, David John

AU - Green, Edward L.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - quantum groups

KW - algebras

KW - varieties

KW - cohomology

KW - coverings

U2 - 10.1093/qmath/hag039

DO - 10.1093/qmath/hag039

M3 - Article

VL - 55

SP - 1

EP - 11

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 1

ER -