Cluster algebra

Summary

A cluster algebra is a commutative ring inside a field of rational functions, generated by special elements called cluster variables. The cluster variables are grouped into overlapping sets of the same size, the clusters. One passes from one cluster to the next by a rule called mutation. Cluster algebras were introduced by Fomin and Zelevinsky. They link the representation theory of quivers, total positivity, Teichmüller theory and combinatorics.