Non-commutative gauge symmetry from strong homotopy algebras

We explicitly construct an L${}_{\mathrm{\infty }}$ algebra that defines U${}_{\star }(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L${}_{\mathrm{\infty }}$ modules. Some possibilities for including P${}_{\mathrm{\infty }}$ algebras are also discussed.