Subproduct systems and C*-algebras

Ge, Y. (2025)

Doctoral Thesis

This thesis studies operator-algebraic aspects of subproduct systems, a generalization of product systems of Hilbert spaces. We examine the Toeplitz and Cuntz--Pimsner C*-algebras attached to a subproduct system and analyze their structure and K-theory. Motivated by quadratic algebras, we introduce quadratic subproduct systems and investigate three natural operations on quadratic algebras. The main results include explicit computations of the K-theory groups of the associated Toeplitz algebras. The proofs use tools from functional analysis, operator algebras, and K-theory, together with combinatorial properties of the underlying subproduct systems. The work shows how the algebraic information of a subproduct system determines invariants of the associated C*-algebras and provides new examples with interesting K-theory.

• Functional analysis
• Operator algebras
• Toeplitz algebras
• Cuntz--Pimsner algebras
• K-theory
• Quadratic algebras
• Arveson--Douglas conjecture

• All authors: Ge, Y.
• Supervisor: Jeu, M.F.E. de
• Co-supervisor: Arici, F.; Gerontogiannis, D.M.
• Committee: Derks, G.; Fiocco, M.; Kakariadis, E.T.A.; Wang, Y.; Yuncken, R.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2025-10-22