A short proof of Kontsevich's cluster conjecture.

DOI10.1016/j.crma.2011.01.004zbMath1266.16026arXiv1011.0245OpenAlexW2963966821WikidataQ123113420 ScholiaQ123113420MaRDI QIDQ627731

Arkady Berenstein, Vladimir S. Retakh

Publication date: 3 March 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0245

zbMATH Keywords

lattice pathsiterations of rational mapsKontsevich cluster conjecturenoncommutative Laurent polynomials

Mathematics Subject Classification ID

Rings arising from noncommutative algebraic geometry (16S38) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Cluster algebras (13F60)

Related Items

The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations. ⋮ Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables ⋮ Noncommutative recursions and the Laurent phenomenon ⋮ Proof of the Kontsevich non-commutative cluster positivity conjecture. ⋮ Rank two non-commutative Laurent phenomenon and pseudo-positivity ⋮ Noncommutative Catalan numbers ⋮ The non-commutative \(A_1T\)-system and its positive Laurent property

Cites Work

• The Laurent phenomenon
• Cluster algebras. II: Finite type classification
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Quantum cluster algebras.
• Cluster algebras I: Foundations
• Discrete Non-commutative Integrability: Proof of a Conjecture by M. Kontsevich
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