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We extend a CDGA $V$ with a perfect pairing of degree $n$ on cohomology to aCDGA $\hat V$ with a pairing of degree $n$ on chain level such that $\hat V$admits a Hodge decomposition and retracts onto $V$ preserving the pairing oncohomology; here we suppose that $V$ is either 1-connected, or that $V$ isconnected, of finite type, and $n$ is odd. We show that a Hodge decompositionof $\hat V$ induces a differential Poincar\'e duality model of $V$ in a naturalway. Assuming that $H(V)$ is 1-connected, we apply our extension to a Sullivanmodel of $V$ in the proof of the existence and "uniqueness" of a 1-connecteddifferential Poincar\'e duality model of $V$ by Lambrechts & Stanley; weeliminate their extra assumptions in the uniqueness statement, including$H^2(V)=0$ if $n$ is odd.

Hodge decompositions and Poincare duality models