A short proof of Kontsevich cluster conjecture

2010/11/01 by Arkady Berenstein, Berenstein, Arkady, Vladimir Retakh +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1011.0245

AMSLaTeX, 3 pages, references updated

openalex publication_date 2010/11/01 · arxiv created 2010/11/10 · arxiv updated 2010/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^-1,(1+y^r)x^-1) are given by noncommutative Laurent polynomials.

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