Abstract
C*-algebras are the (non-commutative) Banach algebras with an involution. Such algebras appear naturally in a dynamical context; see Pedersen [235]. The ones we shall be considering will either be irrational rotation algebras or algebras generated by interval exchange transformations of the unit circle. (The latter we call the Artin rotation algebras; they are canonically isomorphic to the C*-algebras of minimal flows on a surface of genus g >1.)
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Bibligraphic Notes
Operator algebras were introduced by von Neumann in the 30's, see e.g.
J. von Neumann, Zur Algebra der Funktionaloperatoren und Theorie der normalen Operatoren, Math. Annalen 102 (1929), 370-427.
The theory flourished through the influence of pivotal works of I. M. Gelfand and M. Naimark, see
I. M. Gelfand and M. Naimark, On the embedding of normed rings into the ring of operators in Hilbert space, Mat. Sbornik 12 (1943), 197-213.
A. Connes idea of applying such algebras to the study of `dynamics' of foliations has proven to be an effective tool in the area, see
A. Connes, A survey of foliations and operator algebras, Proc. Symp. Pure Math. 38 (1982), 521-627.
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© 2001 Springer-Verlag Berlin Heidelberg
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Nikolaev, I. (2001). C*-Algebras. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_11
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