On the Outer Automorphism Groups of Triangular Alternation Limit Algebras

Let A denote the alternation limit algebra, studied by Hopenwasser and Power and by Poon, which is the closed direct limit of upper triangular matrix algebra determined by refinement embeddings of multiplicity r k and standard embeddings of multiplicity s k. It is shown that the quotient of the isometric automorphism group by the approximately inner automorphisms is the abelian group Zd, where d is the number of primes that are divisors of infinitely many terms of each of the sequences (r k) and (s k). This group is also the group of automorphisms of the fundamental relation of A.