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arXiv · 0911.3051

Reflection groupoids of rank two and Cluster algebras of type $A$

M. Cuntz·I. Heckenberger
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Abstract

We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to `reflection groupoids' by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type $A_{n-3}$ completely describes the set of finite reflection groupoids of rank two with $2n$ objects.

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M. Cuntz, I. Heckenberger. 2009-11-16. Reflection groupoids of rank two and Cluster algebras of type $A$. https://arxiv.org/abs/0911.3051

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