  Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo
constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts
to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a
conjecture on the Campbell-Hausdorff series, which (among other things) extends
the Duflo theorem to germs of bi-invariant distributions on the Lie group $G$.
  The main results of the present paper are as follows. (1) Using a recent
result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for
any Lie group $G$. (2) We give a reformulation of the Kashiwara-Vergne property
in terms of Lie algebra cohomology. As a direct corollary, one obtains the
algebra isomorphism $H(g,S(g)) -> H(g,U(g))$, as well as a more general
statement for distributions.
