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I am trying to learn operator algebra with the view of using them in concrete cases.

So I am looking for references where I can find specific computations on specific example cases, to understand the machinery beyond the concepts (guess what, I am a physicist!). For these examples, I need typically to cover the definition of the initial algebra and the related n.s.f. weight, the representation of the group to be crossed with the algebra, the construction of the cross product, the definition of the cyclic cone, the GMS construction up to the explicit expression of the modular flow of weights.

Are there references (papers, textbook chapters...) where this kind of detail is displayed for what seem to be classical examples such as

  • the crossed-product of the abelian algebra of bounded functions by the the group of integer translations,
  • the crossed product of Araki-Woods by the the group of continuous translations?
  • any other that could make sense from the didactic point of view...

Thanks beforehand !

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