Positivity for cluster algebras

Abstract

We prove the positivity conjecture for all skew-symmetric cluster
algebras.

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      mrnumber = {2534994},
      mrreviewer = {Gregoire Dupont},
      doi = {10.1093/imrn/rnp047},
      volume = {2009},
      zblnumber = {1171.30019},
      }
  • [SZ] Go to document P. Sherman and A. Zelevinsky, "Positivity and canonical bases in rank 2 cluster algebras of finite and affine types," Mosc. Math. J., vol. 4, iss. 4, pp. 947-974, 982, 2004.
    @article{SZ, mrkey = {2124174},
      author = {Sherman, Paul and Zelevinsky, Andrei},
      title = {Positivity and canonical bases in rank 2 cluster algebras of finite and affine types},
      journal = {Mosc. Math. J.},
      fjournal = {Moscow Mathematical Journal},
      volume = {4},
      year = {2004},
      number = {4},
      pages = {947--974, 982},
      issn = {1609-3321},
      mrclass = {16S99 (05E15 22E46)},
      mrnumber = {2124174},
      zblnumber = {1103.16018},
      url = {http://mi.mathnet.ru/eng/mmj/v4/i4/p947},
     

Authors

Kyungyong Lee

Department of Mathematics, Wayne State University, Detroit, MI 48202 and Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, Republic of Korea

Ralf Schiffler

University of Connecticut, Storrs, CT