Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich
Mathematical Physics
2009-09-04 v1 Combinatorics
math.MP
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.0909.0615,
title = {Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich},
author = {P. Di Francesco and R. Kedem},
journal= {arXiv preprint arXiv:0909.0615},
year = {2009}
}
Comments
17 pages, 2 figures