## Extension of spontaneous symmetry breaking of Bost-Connes in case of arbitrary global fields. (Extension du phénomène de brisure spontanée de symétrie de Bost-Connes au cas des corps globaux quelconques.)(French)Zbl 0924.46051

In [C. R. Acad. Sci., Paris, Sér. I 315, 279-284 (1992; Zbl 0781.46045) and Sel. Math., New Ser. 1, 412-457 (1995; Zbl 0842.46040)] J. B. Bost and A. Connes exhibited the phenomenon of spontaneous symmetry breaking in the states of a one-parameter group of automorphisms of a certain Hecke $$C^\ast$$-algebra associated to the field $${\mathbb Q}$$ of rational numbers. The authors extend this work to an arbitrary global field $${\mathbb K}$$, i.e. to any number field or any finite separable extension of the rational field $${\mathbb Z}_p(T)$$. The results are almost literally the same.

### MSC:

 46L55 Noncommutative dynamical systems 81R40 Symmetry breaking in quantum theory 11R42 Zeta functions and $$L$$-functions of number fields 46L35 Classifications of $$C^*$$-algebras

### Citations:

Zbl 0781.46045; Zbl 0842.46040
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