Non-semistable exceptional objects in hereditary categories: Some remarks and conjectures

George Dimitrov, Ludmil Katzarkov

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In our previous paper we studied non-semistable exceptional objects in hereditary categories and introduced the notion of regularity preserving category, but we obtained quite a few examples of such categories. Certain conditions on the Ext-nontrivial couples (exceptional objects X, Y ∈ A with Ext1(X,Y) ≠ 0 and Ext1(Y,X) ≠ 0) were shown to imply regularitypreserving. This paper is a brief review of the previous paper (with emphasis on regularity preserving property) and we add some remarks and conjectures. It is known that in Dynkin quivers Hom(ρ, ρ’) = 0 or Ext1(ρ, ρ’) = 0 for any two exceptional representations. On one hand, in the present paper we prove this fact by a new method, which allows us to extend it to new cases: the extended Dynkin quivers (Formula presented.), which are representation infinite. On the other hand, we use it to show that for any Dynkin quiver Q there are no Ext-nontrivial couples in Repk(Q), which implies regularity preserving of Repk(Q).

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages263-287
Number of pages25
DOIs
StatePublished - 2015
Externally publishedYes

Publication series

NameContemporary Mathematics
Volume643
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Affine quiver
  • Bridgeland stability conditions
  • Dynkin quiver
  • Exceptional collection
  • Exceptional object
  • Representations of quiver

ASJC Scopus subject areas

  • Mathematics(all)

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