Types of quantum field thories
The notion of a net -systems combines the notion of a C-star system with the notion of local net of observables. In this way, the notion of global gauge groups is introduced into the Haag-Kastler approach to AQFT.
so that is a C-star system.
The tupel is a net of -systems if .
This definition makes sense also if the net consists of star-algebras only, of course.
Chapter 6 of: