A short proof of Kontsevich's cluster conjecture

Berenstein, Arkady; Retakh, Vladimir

doi:10.1016/j.crma.2011.01.004

Combinatorics/Algebra

A short proof of Kontsevich's cluster conjecture
[Une courte démonstration d'une conjoncture de Kontsevich]

Présenté par : Maxime Kontsevich

Berenstein, Arkady ¹ ; Retakh, Vladimir ²

¹ Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
² Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA

Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 119-122.

Résumé
Abstract

Nous proposons une démonstration élémentaire d'une conjoncture de Kontsevich qui affirme que l'itération de l'application non-commutative rationnelle $K_{r} : (x, y) \mapsto (x y x^{- 1}, (1 + y^{r}) x^{- 1})$ est donnée par des polynômes de Laurent non-commutatifs.

We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map $K_{r} : (x, y) \mapsto (x y x^{- 1}, (1 + y^{r}) x^{- 1})$ are given by noncommutative Laurent polynomials.

Reçu le : 2010-11-18
Accepté le : 2011-01-04
Publié le : 2011-01-20

DOI : 10.1016/j.crma.2011.01.004

Affiliations des auteurs :

Berenstein, Arkady ¹ ; Retakh, Vladimir ²

¹ Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
² Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA

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Berenstein, Arkady; Retakh, Vladimir. A short proof of Kontsevich's cluster conjecture. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 119-122. doi : 10.1016/j.crma.2011.01.004. http://www.numdam.org/articles/10.1016/j.crma.2011.01.004/

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Cité par

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Cité par Sources :

^☆ The authors were supported in part by the NSF grant DMS #0800247.