Lexicographic TAF Algebras

Abstract

Lexicographic TAF algebras constitute a class of triangular AF algebras which are determined by a countable ordered set Ω \Omega , a dimension function, and a third parameter. While some of the important examples of TAF algebras belong to the class, most algebras in this class have not been studied. The semigroupoid of the algebra, the lattice of invariant projections, the Jacobson radical, and for some cases the automorphism group are computed. Necessary and sufficient conditions for analyticity are given. The results often involve the order properties of the set Ω \Omega .