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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
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