We extend a CDGA V with a perfect pairing of degree n on cohomology to a CDGA \(\hat{V}\) with a pairing of degree n on chain level such that \(\hat{V}\) admits a Hodge decomposition and retracts onto V preserving the pairing on cohomology; here we suppose that V is either 1-connected, or that V is connected, of finite type, and n is odd. We show that a Hodge decomposition of \(\hat{V}\) induces a differential Poincaré duality model of V in a natural way. Assuming that \(\textrm{H}(V)\) is 1-connected, we apply our extension to a Sullivan model of V in the proof of the existence and “uniqueness” of a 1-connected differential Poincaré duality model of V by Lambrechts & Stanley; we eliminate their extra assumptions in the uniqueness statement, including \(\textrm{H}^2(V)=0\) if n is odd.
