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Main Authors:	Berenstein, Arkady, Huang, Min, Retakh, Vladimir
Format:	Preprint
Published:	2025
Subjects:	Representation Theory Algebraic Geometry Combinatorics Quantum Algebra
Online Access:	https://arxiv.org/abs/2507.20393
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author	Berenstein, Arkady Huang, Min Retakh, Vladimir
author_facet	Berenstein, Arkady Huang, Min Retakh, Vladimir
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2507_20393
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries Berenstein, Arkady Huang, Min Retakh, Vladimir Representation Theory Algebraic Geometry Combinatorics Quantum Algebra 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.
title	Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
topic	Representation Theory Algebraic Geometry Combinatorics Quantum Algebra
url	https://arxiv.org/abs/2507.20393

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