English

On cluster algebras from once punctured closed surfaces

Representation Theory 2013-10-17 v1

Abstract

We show that many cluster-theoretic properties of the Markov quiver hold also for adjacency quivers of triangulations of once-punctured closed surfaces of arbitrary genus. Along the way we consider the class P of quivers introduced by Kontsevich and Soibelman, characterize the mutation-finite quivers that belong to that class and draw some conclusions regarding non-degenerate potentials on them.

Keywords

Cite

@article{arxiv.1310.4454,
  title  = {On cluster algebras from once punctured closed surfaces},
  author = {Sefi Ladkani},
  journal= {arXiv preprint arXiv:1310.4454},
  year   = {2013}
}

Comments

17 pages

R2 v1 2026-06-22T01:48:20.845Z