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

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

2009-11-16

arxiv.org/abs/0911.3051v1

Mathematics

Group Theory

18 pages

Scientific paper

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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