Work

Cluster modular groups of affine and doubly extended cluster algebras

Year: 2025

Type: article

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.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-025-03708-8

Authors: Dani Kaufman, Zachary Greenberg

Institutions: University of Copenhagen, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Deutsche Forschungsgemeinschaft, Max-Planck-Institut für Mathematik in den Naturwissenschaften