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The argument shift method is a well-known method for generating commutativefamilies of functions in Poisson algebras from central elements and a vectorfield, verifying a special condition with respect to the Poisson bracket. Inthis notice we give an analogous construction, which gives one a way to createcommutative subalgebras of a deformed algebra from its center (which is as itis well known describable in the terms of the center of the Poisson algebra)and an $L_\infty$-differentiation of the algebra of Hochschild cochains,verifying some additional conditions with respect to the Poisson structure.

$L_\infty$-derivations and the argument shift method for deformation quantization algebras