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 $\beta $ is periodic if and only if $\beta $ has a fixed point in the stability manifold.
Authors
- Anthony Licata (ORCID: https://orcid.org/0000-0003-0290-2393)
- Edmund Heng (ORCID: https://orcid.org/0000-0001-9257-077X)
- Oded Yacobi (ORCID: https://orcid.org/0000-0002-4739-0689)
Institutions
- Australian National University (AU)
- The University of Sydney (AU)
- Australian Mathematical Sciences Institute (AU)
- Australian Centre for International Agricultural Research (AU)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-08-01
- DOI
- https://doi.org/10.1093/imrn/rnaf259
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Foundation for the Advancement of Mesoamerican Studies