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In this paper, we recall the construction from Mackaay–Pan–Tubbenhauer of the algebras Kϵ which allow to understand the sl3 homology for links in a local way (i.e. for tangles). Then, by studying the combinatorics of the Kuperberg bracket, we give a large family of non-elliptic webs whose associated projective modules are indecomposable over these algebras.