Title | **Computing homology using generalized Gröbner bases** |

Author(s) | Becky Eide Hall |

Type | Article in Journal |

Abstract | A well-known theorem due to Manin gives a relationship between modular symbols for a congruence subgroup Γ_0(N) of SL_2(Z) and the homology of the modular curve X_0(N) , making the homology easier to compute. A corresponding theorem of Ash (1992) allows for explicit computation of the homology of congruence subgroups of SL_3(Z) with coefficients in a given representation V. Applying Ashʼs theorem requires finding the invariants of an ideal in the group algebra Z[SL_3(Z)] on V. We employ a generalized notion of Gröbner bases for a non-commutative group algebra in order to determine a minimal generating set for the desired ideal. |

Keywords | Non-commutative group algebra, Gröbner bases, Congruence subgroups, SL 3 ( Z ) |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717113000138 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 54 |

Number | 0 |

Pages | 59 - 71 |

Year | 2013 |

Edition | 0 |

Translation |
No |

Refereed |
No |