Periodic elements in finite type Artin-Tits groups and stability conditions
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 β is periodic if and only if β has a fixed point in the stability manifold.
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