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

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D'Este G., TEKİN AKÇİN H. M.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.48, no.5, pp.2521-2538, 2022 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 48 Issue: 5
• Publication Date: 2022
• Doi Number: 10.1007/s41980-021-00620-9
• Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
• Page Numbers: pp.2521-2538
• Keywords: Tilting modules, Partial tilting modules, Short exact sequences, Quivers, ALGEBRAS
• Open Archive Collection: AVESIS Open Access Collection
• Hacettepe University Affiliated: Yes

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.