Cluster modular groups of affine and doubly extended cluster algebras
Abstract We calculate the cluster modular groups of affine and doubly extended type cluster algebras in a uniform way by introducing a new family of quivers. We use this uniform description to construct a natural finite quotient of the cluster complex of each affine and doubly extended cluster algebra. Using this construction, we introduce the notion of affine and doubly extended generalized associahedra, and count their facets.
Authors
- Dani Kaufman (ORCID: https://orcid.org/0000-0002-1519-6718)
- Zachary Greenberg (ORCID: https://orcid.org/0000-0003-1505-9681)
Institutions
- University of Copenhagen (DK)
- Max Planck Institute for Mathematics in the Sciences (DE)
- Max Planck Institute for Mathematics (DE)
Publication Details
- Journal
- Mathematische Zeitschrift
- Published
- 2025-04-17
- DOI
- https://doi.org/10.1007/s00209-025-03708-8
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Max-Planck-Institut für Mathematik in den Naturwissenschaften