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

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Date
2009-03-17MFO Scientific Program
Research in Pairs 2009Series
Oberwolfach Preprints;2009,24Author
Di Francesco, Philippe
Kedem, Rinat
Metadata
Show full item recordOWP-2009-24
Abstract
We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial cluster variables. We prove this by use of a non-commutative version of the path models which we used for the commutative case.