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Explicit non-inducible rooted cluster morphisms

A mix of human-written and AI-generated textHuman understanding: some partsmath.RA — Rings and Algebras

Contributed by Qiyue Tang

Version 2 / Oct 01, 2026 / CC BY 4.0

Abstract

The augmentation of the Markov cluster algebra is explicit but not inducible as a rooted cluster morphism. This answers a question of Chang and Zhu negatively.

Provenance statement

ChatGPT was used to develop the counterexample and its proof. Codex was used to check the arguments, search the literature, and prepare the manuscript.

References

  1. I. Assem, G. Dupont, and R. Schiffler, On a category of cluster algebras , J. Pure Appl. Algebra 218 (2014), no. 3, 553--582.
  2. J. Beyer and G. Muller, Deep points of cluster algebras , Int. Math. Res. Not. IMRN 2025 (2025), no. 4, rnaf027, 39 pp.
  3. M. Castronovo, M. Gorsky, J. Simental, and D. E. Speyer, Cluster deep loci and mirror symmetry , Commun. Amer. Math. Soc. 6 (2026), 1021--1086; arXiv:2402.16970v2 (https://arxiv.org/abs/2402.16970v2).arXiv
  4. W. Chang and B. Zhu, On rooted cluster morphisms and cluster structures in 22-Calabi--Yau triangulated categories , J. Algebra 458 (2016), 387--421; arXiv:1410.5702v2 (https://arxiv.org/abs/1410.5702v2).arXiv
  5. S. Fomin and A. Zelevinsky, Cluster algebras I: Foundations , J. Amer. Math. Soc. 15 (2002), no. 2, 497--529.
  6. G. Muller, Locally acyclic cluster algebras , Adv. Math. 233 (2013), 207--247.

Version history

  1. v1 · 3 pagesSubmitted by 琪越 唐Initial depositSupersededOct 01, 2026
  2. v2 · 3 pagesSubmitted by Qiyue TangSubmitted as a new versionCurrentNov 06, 2026