  The notion of classical $r$-matrix is re-examined, and a definition suitable
to differential (-difference) Lie algebras, -- where the standard definitions
are shown to be deficient, -- is proposed, the notion of an ${\mathcal
O}$-operator. This notion has all the natural properties one would expect form
it, but lacks those which are artifacts of finite-dimensional isomorpisms such
as not true in differential generality relation $\mbox{End}\, (V) \simeq V^*
\otimes V$ for a vector space $V$. Examples considered include a quadratic
Poisson bracket on the dual space to a Lie algebra; generalized
symplectic-quadratic models of such brackets (aka Clebsch representations); and
Drinfel'd's 2-cocycle interpretation of nondegenate classical $r$-matrices.
