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

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

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-pro...

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Veröffentlicht in:Bulletin of the Iranian Mathematical Society 2022-10, Vol.48 (5), p.2521-2538
Hauptverfasser: D’Este, Gabriella, Akcin, H. Melis Tekin
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung: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.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-021-00620-9