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arXiv · 2107.10334

Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras

Dani Kaufman·Zachary Greenberg
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Abstract

We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex of each affine anddoubly extended cluster algebra. Using this construction, we introduce the notion of affineand doubly extended generalized associahedra, and count their facets.

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Dani Kaufman, Zachary Greenberg. 2025-04-07. Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras. https://arxiv.org/abs/2107.10334

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