TY - JOUR
T1 - Discrete non-commutative integrability
T2 - Proof of a conjecture by M. Kontsevich
AU - Di Francesco, Philippe
AU - Kedem, Rinat
N1 - Funding Information:
We thank M. Kontsevich for explaining his conjectures to us. The research of P.D.F. is supported in part by the ANR Grant GranMa, the ENIGMA research training network MRTN-CT-2004-5652, and the ESF program MISGAM. R.K. is supported by National Science Foundation grant DMS-0802511. This research was hosted by the Mathematisches Forschungsinstitut Oberwolfach and by the IPhT at CEA/Saclay. We thank these institutes for their support.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1093/imrn/rnq024
DO - 10.1093/imrn/rnq024
M3 - Article
AN - SCOPUS:77955645574
SN - 1073-7928
VL - 2010
SP - 4042
EP - 4063
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 21
ER -