| Summary: | Abstract We define a class of A ∞-algebras that are obtained by deformations of higher spin symmetries. While higher spin symmetries of a free CFT form an associative algebra, the slightly broken higher spin symmetries give rise to a minimal A ∞-algebra extending the associative one. These A ∞-algebras are related to non-commutative deformation quantization much as the unbroken higher spin symmetries result from the conventional deformation quantization. In the case of three dimensions there is an additional parameter that the A ∞-structure depends on, which is to be related to the Chern-Simons level. The deformations corresponding to the bosonic and fermionic matter lead to the same A ∞-algebra, thus manifesting the three-dimensional bosonization conjecture. In all other cases we consider, the A ∞-deformation is determined by a generalized free field in one dimension lower.
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