Primitive triangular UHF algebras (Q1276401)

The authors prove that a large class of triangular UHF algebras are primitive. There are cases where explicitly they give a faithful algebraically irreducible representation of the algebra on a separable Hilbert space. For other cases they follow an indirect way studying the prime ideal structure of the algebra. From this they obtain a characterization of the primitive ideal spaces of the lexicographic algebras introduced by \textit{S. C. Power} [Bull. Lond. Math. Soc. 27, No. 3, 273-277 (1995; Zbl 0829.47034)]. More results are given. So a classification up to algebraic isomorphisms of the lexicographic algebras \(A({\mathbb Q}, \nu)\) is obtained.