On a group graded version of BGG

E. L. Green, R. Martínez-Villa, Y. Yoshino

Research output: Contribution to journalArticlepeer-review

Abstract

A major result in Algebraic Geometry is the theorem of Bernstein-Gelfand- Gelfand that states the existence of an equivalence of triangulated categories: grΛ ≅ Db(Coh ℙn), where grΛ 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 languageEnglish
Pages (from-to)3145-3163
Number of pages19
JournalCommunications in Algebra
Volume35
Issue number10
DOIs
Publication statusPublished - Oct 1 2007

Keywords

  • Covering
  • G-graded
  • Koszul

ASJC Scopus subject areas

  • Algebra and Number Theory

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