Realization of two-sided quantum \(K\)-systems. (English) Zbl 0978.82013
Summary: Two-sided quantum \(K\)-systems can be considered on the \(C^*\) and von Neumann level. On the \(C^*\) level examples can be constructed without any obstacles on the basis of first and second quantization. On the von Neumann level, however, \(q\)-deformation in seond quantization prohibits KMS-states. Nevertheless, an example can be found of a two-sided modular \(K\)-system, where the relative commutants are trivial.
MSC:
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 46L60 | Applications of selfadjoint operator algebras to physics |
Keywords:
noncommutative \(C^*\)-algebra; von Neumann algebra; Anosov automorphism; quantum \(K\)-systemsReferences:
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