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In this note, we prove that, for a finite-dimensional Lie algebra  over a field  of characteristic 0 which contains , the Chevalley–Eilenberg complex , which is in a natural way a deformation quantization of the Koszul complex of , is  -quasi-isomorphic to the deformation quantization of the  -bimodule  provided by the Formality Theorem in presence of two branes (Calaque et al., Comput Math 147(01):105–160, ).

The Chevalley–Eilenberg Complex and Deformation Quantization in Presence of Two Branes