Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 105, 39 pages      arXiv:2201.10284      https://doi.org/10.3842/SIGMA.2023.105

Twist Automorphisms and Poisson Structures

Yoshiyuki Kimura a, Fan Qin b and Qiaoling Wei c
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

Received April 03, 2023, in final form December 01, 2023; Published online December 23, 2023

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.

Key words: cluster algebras; twist automorphisms; Poisson algebras.

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