  We consider non-ultra local linear Poisson algebras on a continuous line .
Suitable combinations of representations of these algebras yield
representations of novel generalized linear Poisson algebras or "boundary"
extensions. They are parametrized by a "boundary" scalar matrix and depend in
addition on the choice of an anti-automorphism. The new algebras are the
classical-linear counterparts of known quadratic quantum boundary algebras. For
any choice of parameters the non-ultra local contribution of the original
Poisson algebra disappears. We also systematically construct the associated
classical Lax pair. The classical boundary PCM model is examined as a physical
example.
