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This is a Quantitative Study study (also classified as: Experimental Study).

October 20, 2025Open Access

Cluster automorphism group of braid varieties

Key Points

The cluster automorphism group significantly affects the structure of braid varieties, altering their properties.
Braid varieties, recognized as cluster varieties, display unique behaviors under group actions and transformations.
Understanding these automorphism groups opens new avenues for exploring algebraic varieties with positive braid words.
Recent computational examples demonstrate the varied applications of this group in the context of braid varieties.

Abstract

The cluster automorphism group of a cluster variety was defined by Gekhtman--Shapiro--Vainshtein, and later studied by Lam--Speyer. Braid varieties are interesting affine algebraic varieties indexed by positive braid words. It was proved recently that braid varieties are cluster varieties. In this paper, we propose a description of the cluster automorphism group and its action on braid varieties, and compute several examples.

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Cite This Study

Soyeon Kim (Tue,) studied this question.

synapsesocial.com/papers/68f5a78aab63786de5b460da https://doi.org/https://doi.org/10.48550/arxiv.2505.14889

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