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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 琪越 唐 ↗

Submitter琪越 唐

Version 1 / 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; https://arxiv.org/abs/2402.16970v2 arXiv:2402.16970v2 .arXiv
  4. W. Chang and B. Zhu, On rooted cluster morphisms and cluster structures in $2$-Calabi--Yau triangulated categories , J. Algebra 458 (2016), 387--421; https://arxiv.org/abs/1410.5702v2 arXiv: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. v1Initial depositCurrentOct 01, 2026