Subproduct systems and C*-algebras

Abstract

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.