## Extension techniques in $$C^*$$-cross products by compact group duals and in quantum field theory.(English)Zbl 1035.81032

Summary: Using the methods developed in a previous paper [Rev. Math. Phys. 12, 725–738 (2000; Zbl 1044.81083)], we consider the problem of extending endomorphisms to cross-product by compact group duals getting a result of M. Müger [Ann. Inst. Henri Poincaré Phys. Théor. 71, 359–394 (1999; Zbl 0938.81018)]. Then we discuss some other applications to quantum field theory, mainly in connection with PCT symmetries.

### MSC:

 81T05 Axiomatic quantum field theory; operator algebras 46L60 Applications of selfadjoint operator algebras to physics 46L55 Noncommutative dynamical systems 81R15 Operator algebra methods applied to problems in quantum theory

### Citations:

Zbl 1044.81083; Zbl 0938.81018
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