Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras

2021/07/21 by Dani Kaufman, Kaufman, Dani, Zachary Greenberg +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2107.10334

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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