Extremals and exposed faces of the cone of positive maps

We show that for a matrix A of size n x m, the maps X bar right arrow AXA* and X bar right arrow A X-T A* are extremals of the cone of positive maps acting C-mxm --> C-nxn. When the rank of A equals 1 or m (in which case, necessarily m <= n), we show that these extremals are exposed.