A Note on the Koszul Complex in Deformation Quantization

The aim of this short note is to present a proof of the existence of an A _∞-quasi-isomorphism between the A _∞-S( V ^*)-{wedge(V)} -bimodule K, introduced in Calaque et al. (Bimodules and branes in deformation quantization, 2009), and the Koszul complex K( V) of S( V ^*), viewed as an A _∞-S( V ^*)-{wedge(V)} -bimodule, for V a finite-dimensional (complex or real) vector space.