### Abstract

Let R be the exterior algebra in n + 1 variables over a field K. We study the Auslander-Reiten quiver of the category of linear R-modules, and of certain subcategories of the category of coherent sheaves over P^{n}. If n > 1, we prove that up to shift, all but one of the connected components of these Auslander-Reiten quivers are translation subquivers of a ZA_{∞}- type quiver. We also study locally free sheaves over the projective n-space P^{n} for n > 1 and we show that each connected component contains at most one indecomposable locally free sheaf of rank less than n. Finally, using results from the theory of finite-dimensional algebras, we construct a family of indecomposable locally free sheaves of arbitrary large ranks, where the ranks can be computed using the Chebysheff polynomials of the second kind.

Original language | English (US) |
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Pages (from-to) | 397-408 |

Number of pages | 12 |

Journal | Compositio Mathematica |

Volume | 142 |

Issue number | 2 |

DOIs | |

State | Published - Dec 19 2006 |

### Keywords

- Coherent sheaves
- Exterior algebra
- Koszul algebras
- Linear modules
- Locally free sheaves

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Compositio Mathematica*,

*142*(2), 397-408. https://doi.org/10.1112/S0010437X05001703