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arXiv · 2502.20711

Periodic elements in finite type Artin-Tits groups and stability conditions

Edmund Heng·Anthony M. Licata·Oded Yacobi
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Abstract

Periodic elements in finite type Artin--Tits groups are elements some positive power of which is central. We give a dynamical characterisation of periodic elements via their action on the corresponding 2-Calabi--Yau category and on its space of (fusion equivariant) Bridgeland stability conditions. The main theorem is that an element $\beta$ is periodic if and only if $\beta$ has a fixed point in the stability manifold.

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Edmund Heng, Anthony M. Licata, Oded Yacobi. 2025-02-28. Periodic elements in finite type Artin-Tits groups and stability conditions. https://arxiv.org/abs/2502.20711

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