# Quivers without loops admit global dimension 2

Nicolas Poettering

Number | 47 |
---|---|

Author | Nicolas Poettering |

Project | C01 |

Year | 2010 |

Let Q be a finite quiver without loops. Then there is an admissible ideal I such that the algebra kQ/I has global dimension at most two and is (strongly) quasi-hereditary. In addition some other (strongly) quasi-hereditary algebras kQ/I' are constructed with bigger global dimension.