I will introduce the Bost-Connes C*-dynamical system from Number Theory exhibiting a phase transition with spontaneous symmetry breaking. The key ingredient in their construction is a Hecke algebra, obtained from the ring inclusion of the integers in the rationals. I will show how this Hecke algebra can be realized as a semigroup crossed product, and how this alternative description can be used to elucidate its structure and to simplify the study of equilibrium.

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Created: 2/21/01 Updated: 2/21/01