Auslander-Reiten sequences, locally free sheaves and Chebysheff polynomials

Roberto Martínez-Villa, Dan Zacharia

Research output: Contribution to journalArticle

4 Scopus citations

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 Pn. 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 Pn 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 languageEnglish (US)
Pages (from-to)397-408
Number of pages12
JournalCompositio Mathematica
Volume142
Issue number2
DOIs
StatePublished - Dec 19 2006

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Auslander-Reiten sequences, locally free sheaves and Chebysheff polynomials'. Together they form a unique fingerprint.

  • Cite this