Discrete non-commutative integrability: Proof of a conjecture by M. Kontsevich

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Abstract

We prove a conjecture of Kontsevich regarding the solutions of rank 2 recursion relations for non-commutative variables, which, in the commutative case, reduce to rank 2 cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial cluster variables. We prove this by the use of a non-commutative version of the path models, which we used for the commutative case.

Original languageEnglish (US)
Pages (from-to)4042-4063
Number of pages22
JournalInternational Mathematics Research Notices
Volume2010
Issue number21
DOIs
StatePublished - Nov 11 2010

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Integrability
Positive Polynomials
Cluster Algebra
Laurent Polynomials
Recursion Relations
Path
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Discrete non-commutative integrability : Proof of a conjecture by M. Kontsevich. / Di Francesco, Philippe; Kedem, Rinat.

In: International Mathematics Research Notices, Vol. 2010, No. 21, 11.11.2010, p. 4042-4063.

Research output: Contribution to journalArticle

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