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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 105, 39 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.105 (Mi sigma2000) 		 
Twist Automorphisms and Poisson Structures

Yoshiyuki Kimuraa, Fan Qinb, Qiaoling Weic

a Faculty of Liberal Arts, Sciences and Global Education, Osaka Metropolitan University, Japan
b School of Mathematical Sciences, Beijing Normal University, P.R. China
c School of Mathematical Sciences, Capital Normal University, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2023.105
Abstract: 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.
Keywords: cluster algebras, twist automorphisms, Poisson algebras.
Funding agency Grant number
Japan Society for the Promotion of Science 17K14168
22H01114
National Natural Science Foundation of China 12271347
The first author is supported by JSPS KAKENHI Grant Number 17K14168 and 22H01114. The second author is supported by NSFC Grant Number 12271347.
Received: April 3, 2023; in final form December 1, 2023; Published online December 23, 2023
Document Type: Article
MSC: 13F60, 17B63
Language: English
Citation: Yoshiyuki Kimura, Fan Qin, Qiaoling Wei, “Twist Automorphisms and Poisson Structures”, SIGMA, 19 (2023), 105, 39 pp.
Citation in format AMSBIB
\Bibitem{KimQinWei23}
\by Yoshiyuki~Kimura, Fan~Qin, Qiaoling~Wei
\paper Twist Automorphisms and Poisson Structures
\jour SIGMA
\yr 2023
\vol 19
\papernumber 105
\totalpages 39
\mathnet{http://mi.mathnet.ru/sigma2000}
\crossref{https://doi.org/10.3842/SIGMA.2023.105}
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