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- W2254030809 abstract "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." @default.
- W2254030809 created "2016-06-24" @default.
- W2254030809 creator A5037448638 @default.
- W2254030809 date "2016-01-28" @default.
- W2254030809 modified "2023-09-23" @default.
- W2254030809 title "Positivity for quantum cluster algebras" @default.
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- W2254030809 doi "https://doi.org/10.48550/arxiv.1601.07918" @default.
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