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Positivity for quantum cluster algebras
Annals of Mathematics
Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew-symmetric quantum cluster algebras, via a proof of a conjecture first suggested by Kontsevich on the purity of mixed Hodge structures arising in the theory of cluster mutation of spherical collections in 3-Calabi-Yau categories. The result implies positivity, as well as the stronger Lefschetz property conjectured by Efimov, and also the classical positivitydoi:10.4007/annals.2018.187.1.3 fatcat:dy7srwtlgndh3f7whirpzl4bq4