Abstract
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 A ̃ which is an incidence algebra of the associated partially ordered set P ̃ 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 M n ( K) to be strongly graded by a group G and coefficient ring A containing n primitive, orthogonal idempotents.
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