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.
Original language | English (US) |
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Pages (from-to) | 615-691 |
Number of pages | 77 |
Journal | Annals of Combinatorics |
Volume | 27 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2023 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Keywords
- Cluster algebras
- Generalized cluster algebras
- Scattering diagrams
- Theta functions