Cuntz-Pimsner algebras associated with substitution tilings

• Main Author: Williamson, Peter
• Other Authors: Putnam, Ian Fraser
• Language: English; en
• Published: 2017
• Subjects: mathematics; tiling spaces; c* algebras; hilbert modules; cuntz-pimsner algebras
• Online Access: http://hdl.handle.net/1828/7711

A Cuntz-Pimsner algebra is a quotient of a generalized Toeplitz algebra. It is completely determined by a C*-correspondence, which consists of a right Hilbert A- module, E, and a *-homomorphism from the C*-algebra A into L(E), the adjointable operators on E. Some familiar examples of C*-algebras which can be recognized as Cuntz-Pimsner algebras include the Cuntz algebras, Cuntz-Krieger algebras, and crossed products of a C*-algebra by an action of the integers by automorphisms. In this dissertation, we construct a Cuntz-Pimsner Algebra associated to a dynam- ical system of a substitution tiling, which provides an alternate construction to the groupoid approach found in [3], and has the advantage of yielding a method for com- puting the K-Theory. === Graduate