Caldero-Chapoton algebras

@article{Irelli2012CalderoChapotonA,
  title={Caldero-Chapoton algebras},
  author={Giovanni Cerulli Irelli and Daniel Labardini-Fragoso and Jan Schroer},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={367},
  pages={2787-2822}
}
Motivated by the representation theory of quivers with potential introduced by Derksen, Weyman and Zelevinsky and by work of Caldero and Chapoton, who gave explicit formulae for the cluster variables of Dynkin quivers, we associate a CalderoChapoton algebra AΛ to any (possibly infinite dimensional) basic algebra Λ. By definition, AΛ is (as a vector space) generated by the Caldero-Chapoton functions CΛ(M) of the decorated representations M of Λ. If Λ = P(Q,W ) is the Jacobian algebra defined by… Expand

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