The Picard group of a structural matrix algebra Original Research Article

We investigate the Picard group of a structural matrix (or incidence) algebra A of a finite preordered set P over a field and we consider five interrelated problems. Our main technique involves establishing a connection between the group of outer automorphisms Out(A) of A and the group of outer automorphisms of the basic algebra à which is an incidence algebra of the associated partially ordered set image of P. We discuss necessary and sufficient conditions for Out(A) to be a natural invariant for the Morita equivalence class of A, and necessary and sufficient conditions for Mn(K) to be strongly graded by a group G and coefficient ring A containing n primitive, orthogonal idempotents.