Year
2014
Degree Name
Doctor of Philosophy
Department
School of Mathematics and Applied Statistics
Recommended Citation
Li, Hui, Twisted topological graph algebras, Doctor of Philosophy thesis, School of Mathematics and Applied Statistics, University of Wollongong, 2014. https://ro.uow.edu.au/theses/4085
Abstract
We generalize Katsura's graph correspondence associated to a topological graph by incorporating a 1-cocycle on the edge set of the graph and constructing a C*-correspondence called the twisted graph correspondence. We investigate the Cuntz-Pimsner algebra of the twisted graph correspondence by introducing covariant twisted Toeplitz representations of the graph, and showing that the Cuntz-Pimsner algebra of the twisted graph correspondence is generated by a universal covariant twisted Toeplitz representation of the graph. We expand on Katsura's ideas to prove fundamental results about the Cuntz-Pimsner algebra of the twisted graph correspondence. In particular we establish a version of the Cuntz-Krieger Uniqueness Theorem, and study the ideal structure.
Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.