C*-algebras of graphs of semigroups

Chen, Cheng (2021) C*-algebras of graphs of semigroups. PhD thesis, University of Glasgow.

Abstract

In the thesis, we investigate the properties of the reduced C*-algebras of graphs of monoids. These include nuclearity, ideal structure, K-theory and so on.

Based on Serre’s definitions of graphs of groups and their fundamental groups, we define graphs of monoids and study the right LCM property. We also investigate the nuclearity of C*-algebras of graphs of monoids and give some examples to embed some special graphs of monoids (generalised Baumslag-Solitar monoids) into amenable groups.

Using Xin Li’s work to view reduced semigroup C*-algebras as reduced groupoid C*-algebras, we study the topological approximate invariant means, the closed subgroupoids and the principality of the associated groupoids. The results in this part help us work out the primitive ideal spaces of these groupoid C*-algebras. Lastly, we compute K-theory of all the groupoid C*-algebras induced by the associated groupoids and their closed subgroupoids.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from the China Scholarship Council (CSC).
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Li, Professor Xin and Whittaker, Professor Mike
• Date of Award: 2021
• Depositing User: Theses Team
• Unique ID: glathesis:2021-82596
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 21 Dec 2021 10:11
• Last Modified: 08 Apr 2022 17:01
• Thesis DOI: 10.5525/gla.thesis.82596
• URI: https://theses.gla.ac.uk/id/eprint/82596