LEXICOGRAPHIC TAF ALGEBRAS

Lexicographic TAF algebras constitute a class of triangular AF algebra s which are determined by a countable ordered set Omega, a dimension f unction, and a third parameter. While some of the important examples o f TAF algebras belong to the class, most algebras in this class have n ot been studied. The semigroupoid of the algebra, the lattice of invar iant projections, the Jacobson radical, and for some cases the automor phism group are computed. Necessary and sufficient conditions for anal yticity are given. The results often involve the order properties of t he set Omega.