Cuntz-Pimsner algebras associated with substitution tilings
Date
2017-01-03
Authors
Williamson, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.
Description
Keywords
mathematics, tiling spaces, c* algebras, hilbert modules, cuntz-pimsner algebras