### Abstract

A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand- Gelfand that states the existence of an equivalence of triangulated categories: gr_{Λ} ≅ Db(Coh ℙn), where gr_{Λ} denotes the stable category of finitely generated graded modules over the n + 1 exterior algebra and Db(Coh ℙn) is the derived category of bounded complexes of coherent sheaves on projective space ℙn. Generalizations of this result were obtained in Martínez-Villa and Saorín (2004) and from a different point of view, the theorem has been extended by Yanagawa (2004) to ℤn-graded modules over the polynomial algebra. This generalization has important applications in combinatorial commutative algebra. The aim of the article is to extend the results of Martínez-Villa and Saorín (2004) to group graded algebras in order to obtain a generalization of Yanagawa's results having in mind the application to other settings (Geigle and Lenzing, 1987).

Original language | English |
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Pages (from-to) | 3145-3163 |

Number of pages | 19 |

Journal | Communications in Algebra |

Volume | 35 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2007 |

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### Keywords

- Covering
- G-graded
- Koszul

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*35*(10), 3145-3163. https://doi.org/10.1080/00914030701409825