Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913987435692032 |
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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 |