Automorphism groups of algebras of triangular matrices

Abstract

If A is an algebra of n X n matrices over an integral domain, we can associate with A a graph whose edges are pairs (i, j) such that the (i, j) entry of every element of A is zero. The graph in turn defines a group of permutations and automorphisms of A which are conjugations by permutations matrices. For a suitably restricted class of algebras A we show that the automorphism group of A is the semidirect product of this group of permutation matrices with the subgroup of inner automorphisms.