## Introduction to C*-algebras

### Dr. Gherardo Piacitelli

Contents

- Definition of C*-algebra. Gelfand transform, functional calculus, representation theory. GNS construction. Universal representation. Geometry of states
- Operator algebras: Von Neumann Algebras. Weak topology, bicommutant theorem, classification of factors.
- Noncommutative integration. Tomita-Takesaki theory and applications to statistical mechanics. KMS states and applications.
- Tensor C* categories and application to superselection theory in local quantum physics.