On a group graded version of BGG

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

Research output: Contribution to journalArticle

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 2007

Fingerprint

Graded Module
Exterior Algebra
Triangulated Category
Coherent Sheaf
Polynomial Algebra
Derived Category
Graded Algebra
Algebraic Geometry
Commutative Algebra
Group Algebra
Projective Space
Theorem
Finitely Generated
Equivalence
Denote
Generalization

Keywords

  • Covering
  • G-graded
  • Koszul

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On a group graded version of BGG. / Green, E. L.; Martínez-Villa, R.; Yoshino, Yuji.

In: Communications in Algebra, Vol. 35, No. 10, 10.2007, p. 3145-3163.

Research output: Contribution to journalArticle

Green, EL, Martínez-Villa, R & Yoshino, Y 2007, 'On a group graded version of BGG', Communications in Algebra, vol. 35, no. 10, pp. 3145-3163. https://doi.org/10.1080/00914030701409825
Green, E. L. ; Martínez-Villa, R. ; Yoshino, Yuji. / On a group graded version of BGG. In: Communications in Algebra. 2007 ; Vol. 35, No. 10. pp. 3145-3163.
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