Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras

Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras

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Title: Actions of Finite Groups on Substitution Tilings and Their Associated C*-algebras
Author: Starling, Charles B
Abstract: The goal of this thesis is to examine the actions of finite symmetry groups on aperiodic tilings. To an aperiodic tiling with finite local complexity arising from a primitive substitution rule one can associate a metric space, transformation groupoids, and C*-algebras. Finite symmetry groups of the tiling act on each of these objects and we investigate appropriate constructions on each, namely the orbit space, semidirect product groupoids, and crossed product C*-algebras respectively. Of particular interest are the crossed product C*-algebras; we derive important structure results about them and compute their K-theory.
Date: 2012
URI: http://hdl.handle.net/10393/20663
Supervisor: Giordano, Thierry
Faculty: Sciences / Science
Degree: PhD

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