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- Ryan J. Zerr
- Int. J. Math. Mathematical Sciences
- 2005

For certain AF algebras, a topological space is described which provides an isomorphism invariant for the algebras in this class. These AF algebras can be described in graphi-cal terms by virtue of the existence of a certain type of Bratteli diagram, and the order-preserving automorphisms of the corresponding AF algebra's dimension group are then studied by… (More)

- RYAN J. ZERR
- 2003

We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C *-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific… (More)

- RYAN J. ZERR
- 2003

A method is described which identifies a wide variety of AF algebra dimension groups with groups of continuous functions. Since the continuous functions in these groups have domains which correspond to the set of all infinite paths in what will be called minimal Bratteli diagrams, it becomes possible, in some cases, to analyze the dimension group's order… (More)

- RYAN J. ZERR
- 2006

An important and widely studied class of operator algebras is the approximately finitedimensional (AF) C∗-algebras. Their name stems from the fact that each element of the algebra can be approximated, to arbitrary precision, by an element from a finitedimensional subalgebra. As such elements are direct sums of matrices, the AF algebras can be thought of as… (More)

The Ducci map applied to vectors in R 3 is considered. It is shown that for any starting vector, the corresponding sequence of iterates either eventually becomes periodic or, if not eventually periodic, asymptotically approaches the zero vector. A precise characterization of which vectors exhibit each of these separate behaviors is given.

- Ryan J. Zerr
- Int. J. Math. Mathematical Sciences
- 2006

A method is described which identifies a wide variety of AF algebra dimension groups with groups of continuous functions. The results here generalize the well-known fact that commutative AF algebras have dimension groups which can be identified with groups of integer-valued continuous functions.

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