A Bijection Between the Indecomposable Summands of Two Multiplicity Free Tilting Modules


D'Este G., TEKİN AKÇİN H. M.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1007/s41980-021-00620-9
  • Title of Journal : BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Keywords: Tilting modules, Partial tilting modules, Short exact sequences, Quivers, ALGEBRAS

Abstract

We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules X and Y. This bijection fixes the common indecomposable summands of X and Y and sends indecomposable projective (resp., injective) summands of exactly one module to non-projective (resp., non-injective) summands of the other. Moreover, this bijection interchanges the two possible non-isomorphic complements of an almost complete tilting module.