On cycles of length three

2021/02/16 by Chaio, Claudia, Guazzelli, Victoria, Suarez, Pamela · 2 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2102.08216

Abstract

We prove that if A is a string algebra then there are not three irreducible morphisms between indecomposable A-modules such that its composition belongs to \Re⁶ \backslash \Re⁷, whenever the compositions of two of them are not in \Re³. Moreover, for any positive integer n ≥ 3, we show that there are n irreducible morphisms such that their composition is in \Reⁿ⁺⁴ \backslash \Reⁿ⁺⁵.

Cited by

• Leaps in the depth of compositions of irreducible morphisms
• On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms

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