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arXiv · 2507.20393

Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries

Arkady Berenstein·Min Huang·Vladimir Retakh
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Abstract

The aim of the paper is to define noncommutative cluster structure on several algebras ${\mathcal A}$ related to marked surfaces possibly with orbifold points of various orders, which includes noncommutative clusters, i.e., embeddings of a given group $G$ into the multiplicative monoid ${\mathcal A}^\times$ and an action of a certain braid-like group $Br_{\mathcal A}$ by automorphisms of each cluster group in a compatible way. For punctured surfaces we construct new symmetries, noncommutative tagged clusters and establish a noncommutative Laurent Phenomenon.

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BibTeXRIS

Arkady Berenstein, Min Huang, Vladimir Retakh. 2025-07-27. Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries. https://arxiv.org/abs/2507.20393

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