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

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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
Issue number21
StatePublished - Nov 11 2010


ASJC Scopus subject areas

  • Mathematics(all)

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