Proof of the Kontsevich non-commutative cluster positivity conjecture.

DOI10.1016/j.crma.2012.10.034zbMath1266.16028arXiv1201.3426OpenAlexW1985744704WikidataQ122860689 ScholiaQ122860689MaRDI QIDQ694676

Dylan Rupel

Publication date: 13 December 2012

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

Full work available at URL: https://arxiv.org/abs/1201.3426

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 (11)

The existence of greedy bases in rank 2 quantum cluster algebras ⋮ Positivity for cluster algebras of rank 3 ⋮ Quantum cluster characters for valued quivers ⋮ Greedy bases in rank 2 quantum cluster algebras ⋮ Greedy elements in rank 2 cluster algebras ⋮ The greedy basis equals the theta basis: A rank two haiku ⋮ Noncommutative recursions and the Laurent phenomenon ⋮ Rank two non-commutative Laurent phenomenon and pseudo-positivity ⋮ Quantum cluster characters of Hall algebras ⋮ The non-commutative \(A_1T\)-system and its positive Laurent property ⋮ Positivity for cluster algebras

Cites Work

• A short proof of Kontsevich's cluster conjecture.
• Non-commutative integrability, paths and quasi-determinants
• Quantum cluster algebras.
• Cluster algebras I: Foundations
• Discrete Non-commutative Integrability: Proof of a Conjecture by M. Kontsevich

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