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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/24315

Title: Dimension Groups and C*-algebras Associated to Multidimensional Continued Fractions
Authors: Maloney, Gregory
Advisor: Elliott, George Arthur
Department: Mathematics
Keywords: dimension group
C*-algebra
continued fraction
multidimensional continued fraction
Issue Date: 13-Apr-2010
Abstract: Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion. There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group. We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.
URI: http://hdl.handle.net/1807/24315
Appears in Collections:Doctoral
Department of Mathematics - Doctoral theses

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