Tilting Theory: A Gift of Representation Theory to Mathematics

D'Este, Gabriella

doi:10.1007/s00283-017-9733-y

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2021

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Cited by 2 publications

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“…If (4) holds, then we deduce from Lemma 2.1 that M n+1 ∈ addL. This remark and (5) imply that in both cases M is not multiplicity free. This implies that (6) W is not multiplicity free.…”

Section: Resultsmentioning

confidence: 70%

A bijection between the indecomposable summands of two multiplicity free tilting modules

D'Este¹,

Akcin²

2021

Preprint

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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.

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“…If (4) holds, then we deduce from Lemma 2.1 that M n+1 ∈ addL. This remark and (5) imply that in both cases M is not multiplicity free. This implies that (6) W is not multiplicity free.…”

Section: Resultsmentioning

confidence: 70%