The Picard group of a structural matrix algebra

We investigate the Picard group of a structural matrix (or incidence) algeb ra A of a finite preordered set P over a field and we consider five interre lated problems. Our main technique involves establishing a connection betwe en the group of outer automorphisms Out(A) of A and the group of outer auto morphisms of the basic algebra (A) over tilde which is an incidence algebra of the associated partially ordered set (P) over tilde of P. We discuss ne cessary and sufficient conditions for Out(A) to be a natural invariant for the Morita equivalence class of A, and necessary and sufficient conditions for M-n(K) to be strongly graded by a group G and coefficient ring A contai ning n primitive, orthogonal idempotents. (C) 2000 Published by Elsevier Sc ience Inc. All rights reserved.