Geodesic
Positivity for quantum cluster algebras
Ben Davison1
1 School of Mathematics and Statistics University of Glasgow, University Place Glasgow, United Kingdom
Annals of mathematics, Tome 187 (2018) no. 1, pp. 157-219

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 positivity conjecture of Fomin and Zelevinsky, recently proved by Lee and Schiffler. Closely related to these results is a categorified “no exotics” type theorem for cohomological Donaldson–Thomas invariants, which we discuss and prove in the appendix.

DOI : 10.4007/annals.2018.187.1.3

Ben Davison 1

1 School of Mathematics and Statistics University of Glasgow, University Place Glasgow, United Kingdom 
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Ben Davison. Positivity for quantum cluster algebras. Annals of mathematics, Tome 187 (2018) no. 1, pp. 157-219. doi: 10.4007/annals.2018.187.1.3

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