A natural map from the graded Legendrian skein algebra of a surface to the Hall algebra of its Fukaya category is an isomorphism for disks with marked points and injective for annuli.
On the Fukaya categories of higher genus surfaces
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Legendrian skein algebras and Hall algebras
A natural map from the graded Legendrian skein algebra of a surface to the Hall algebra of its Fukaya category is an isomorphism for disks with marked points and injective for annuli.