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

Creative Commons License

D'Este G., TEKİN AKÇİN H. M.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.48, sa.5, ss.2521-2538, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41980-021-00620-9
  • Dergi Adı: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2521-2538
  • Anahtar Kelimeler: Tilting modules, Partial tilting modules, Short exact sequences, Quivers, ALGEBRAS
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.