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arXiv · 2607.08609

Proof of Rump's Retraction Conjecture for Quasilinear Cycle Sets

Carsten Dietzel
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Abstract

Nondegenerate cycle sets were introduced by Rump as an algebraic framework for nondegenerate, involutive solutions to the Yang--Baxter equation. Nondegenerate cycle set structures on abelian groups, such as translation-invariant and quasilinear cycle sets, are of particular interest when studying the retraction problem in the theory of the Yang--Baxter equation. In this article, we solve the retraction problem for finite quasilinear cycle sets by showing that each nontrivial quasilinear cycle set is retractable, thus proving a conjecture of Rump.

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Carsten Dietzel. 2026-07-09. Proof of Rump's Retraction Conjecture for Quasilinear Cycle Sets. https://arxiv.org/abs/2607.08609

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