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arXiv · 2201.10284

Twist automorphisms and Poisson structures

Yoshiyuki Kimura·Fan Qin·Qiaoling Wei
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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.

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Yoshiyuki Kimura, Fan Qin, Qiaoling Wei. 2022-01-25. Twist automorphisms and Poisson structures. https://doi.org/10.3842/sigma.2023.105

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