Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras
Combinatorics
2022-11-29 v3 Commutative Algebra
Algebraic Geometry
Quantum Algebra
Representation Theory
Abstract
We give a construction of generalized cluster varieties and generalized cluster scattering diagrams for reciprocal generalized cluster algebras, the latter of which were defined by Chekhov and Shapiro. These constructions are analogous to the structures given for ordinary cluster algebras in the work of Gross, Hacking, Keel, and Kontsevich. As a consequence of these constructions, we are also able to construct theta functions for generalized cluster algebras, again in the reciprocal case, and demonstrate a number of their structural properties.
Keywords
Cite
@article{arxiv.2110.08157,
title = {Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras},
author = {Man-Wai Mandy Cheung and Elizabeth Kelley and Gregg Musiker},
journal= {arXiv preprint arXiv:2110.08157},
year = {2022}
}
Comments
Updated to reflect reviewers' comments and to use the preferred journal formatting