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

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

2009-09-03

arxiv.org/abs/0909.0615v1

Physics

Mathematical Physics

17 pages, 2 figures

Scientific paper

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.

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