  The task to construct parametrices of elliptic differential operators on a
manifold with edges requires a calculus of operators with a two-component
principal symbolic hierarchy, consisting of (edge-degenerate) interior and
(operator-valued) edge symbols. This so-called edge-algebra can be interpreted
as a generalisation of the (pseudo-differential) algebra of boundary value
problems without the transmission property at the boundary. We study new
properties of the edge-algebra, in particular, what concerns the role of Green
operators and their kernel representations.
