On The Automorphisms of Cluster Algebras

Details On The Automorphisms of Cluster Algebras On The Automorphisms of Cluster Algebras

2010-11-03

arxiv.org/abs/1011.0894v1

Mathematics

Representation Theory

Scientific paper

Let $A_{n}(S)$ be a coefficient free cluster algebra over a field $K$. A
cluster automorphism is an element of $Aut._{K}K(t_{1}, t_{2},..., t_{n})$
which leaves the set of all cluster variables, $\xi_{S}$, invariant. The group
of all such automorphisms is studied in terms of the orbits of the symmetric
group action on the set of all seeds S and the cluster pattern.

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