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arXiv · 2110.08157

Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras

Man-Wai Mandy Cheung·Elizabeth Kelley·Gregg Musiker
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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.

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Man-Wai Mandy Cheung, Elizabeth Kelley, Gregg Musiker. 2021-10-15. Cluster scattering diagrams and theta functions for reciprocal generalized cluster algebras. https://arxiv.org/abs/2110.08157

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