Twist Automorphisms and Poisson Structures
We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their compatibility with Poisson structures and quantization. The twist...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212026 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twist Automorphisms and Poisson Structures. Yoshiyuki Kimura, Fan Qin and Qiaoling Wei. SIGMA 19 (2023), 105, 39 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862664335266938880 |
|---|---|
| author | Kimura, Yoshiyuki Qin, Fan Wei, Qiaoling |
| author_facet | Kimura, Yoshiyuki Qin, Fan Wei, Qiaoling |
| citation_txt | Twist Automorphisms and Poisson Structures. Yoshiyuki Kimura, Fan Qin and Qiaoling Wei. SIGMA 19 (2023), 105, 39 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their compatibility with Poisson structures and quantization. The twist automorphisms always permute well-behaved bases for cluster algebras. We explicitly construct (quantum) twist automorphisms of Donaldson-Thomas type and for principal coefficients.
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| first_indexed | 2026-03-16T07:17:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212026 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T07:17:18Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kimura, Yoshiyuki Qin, Fan Wei, Qiaoling 2026-01-23T10:07:44Z 2023 Twist Automorphisms and Poisson Structures. Yoshiyuki Kimura, Fan Qin and Qiaoling Wei. SIGMA 19 (2023), 105, 39 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 17B63 arXiv:2201.10284 https://nasplib.isofts.kiev.ua/handle/123456789/212026 https://doi.org/10.3842/SIGMA.2023.105 We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their compatibility with Poisson structures and quantization. The twist automorphisms always permute well-behaved bases for cluster algebras. We explicitly construct (quantum) twist automorphisms of Donaldson-Thomas type and for principal coefficients. The authors express their sincere thanks to the anonymous referees for their insightful comments and constructive suggestions. The first author is supported by JSPS KAKENHI Grant Numbers 17K14168 and 22H01114. The second author is supported by NSFC Grant Number 12271347. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twist Automorphisms and Poisson Structures Article published earlier |
| spellingShingle | Twist Automorphisms and Poisson Structures Kimura, Yoshiyuki Qin, Fan Wei, Qiaoling |
| title | Twist Automorphisms and Poisson Structures |
| title_full | Twist Automorphisms and Poisson Structures |
| title_fullStr | Twist Automorphisms and Poisson Structures |
| title_full_unstemmed | Twist Automorphisms and Poisson Structures |
| title_short | Twist Automorphisms and Poisson Structures |
| title_sort | twist automorphisms and poisson structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212026 |
| work_keys_str_mv | AT kimurayoshiyuki twistautomorphismsandpoissonstructures AT qinfan twistautomorphismsandpoissonstructures AT weiqiaoling twistautomorphismsandpoissonstructures |