Geodesic
Shifts on Type II 1 Factors
Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 492-511

Voir la notice de l'article provenant de la source Cambridge University Press

A shift on a unital C*-algebras is a *-endomorphism α of which fixes the identity and has the property that the intersection of the ranges of αn for n = 1, 2, 3, ... consists only of multiples of the identity. In [4] R. T. Powers introduced the notion of a shift on a C*-algebra and considered both discrete and continuous one-parameter semi-groups of shifts. In this paper we focus on discrete shifts. We use a construction of Powers to obtain shifts on certain unital AF C*-algebras. These are defined by constructing a set {ui:i = 1, 2, ...} of self-adjoint unitary operators which pairwise either commute or anticommute. Setting α(ui) = ui + 1 , determines an endomorphism on the group algebra generated by the ui 's. This algebra is called a binary shift algebra. By passing to the (unique) C*-algebra completion we obtain an AF-algebra on which a defines a shift. 
Price, Geoffrey L. Shifts on Type II 1 Factors. Canadian journal of mathematics, Tome 39 (1987) no. 2, pp. 492-511. doi: 10.4153/CJM-1987-021-2
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[1] 1. Bratteli, O., Inductive limits of finite-dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. Google Scholar

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[3] 3. Jones, V. F. R., Index for subfactors, Invent. Math. 72 (1983), 1–25. Google Scholar

[4] 4. Powers, R. T., An index theory for semigroups of *-endomorphisms of B(H) and type II factors, Can. J. Math., to appear Google Scholar | DOI

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