Abstract
We consider strongly maximal triangular subalgebras of AF algebras. These are the triangular algebras [Formula: see text] such that [Formula: see text] is dense in the ambient AF algebra. We prove that every isometric isomorphism between two strongly maximal triangular subalgebras of the AF algebra [Formula: see text] factors as the composition of two automorphsims of [Formula: see text], one induced by a homeomorphism of the Gelfand spectrum of the diagonal of [Formula: see text], and the other induced by a cocycle on the groupoid supporting [Formula: see text]. As a consequence we obtain that the partial order supporting [Formula: see text] is an isomorphism invariant for [Formula: see text]. Another result establishes conditions that if satisfied by a strongly maximal triangular subalgebra [Formula: see text] of a UHF algebra guarantee that [Formula: see text] is product type analytic. As a consequence we show that the two fundamental examples of triangular UHF algebras are product type analytic, and we exhibit cocycles implementing the analyticity.
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