Bost–Connes system
In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related to the Dedekind zeta function of the number field. {{harvtxt|Bost|Connes|1995}} introduced Bost–Connes systems by constructing one for the rational numbers. {{harvtxt|Connes|Marcolli|Ramachandran|2005}} extended the construction to imaginary quadratic fields.
Such systems have been studied for their connection with Hilbert's Twelfth Problem. In the case of a Bost–Connes system over Q, the absolute Galois group acts on the ground states of the system.
References
- {{Citation | last1=Bost | first1=J.-B. | author1-link=Jean-Benoît Bost | last2=Connes | first2=Alain | author2-link=Alain Connes | title=Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory | doi=10.1007/BF01589495 | mr=1366621 | year=1995 | journal=Selecta Mathematica |series=New Series | issn=1022-1824 | volume=1 | issue=3 | pages=411–457| s2cid=116418599 | url=https://cds.cern.ch/record/283504/files/SCAN-9506164.pdf }}
- {{Citation | last1=Connes | first1=Alain | author1-link=Alain Connes | last2=Marcolli | first2=Matilde | author2-link=Matilde Marcolli | last3=Ramachandran | first3=Niranjan | title=KMS states and complex multiplication | doi=10.1007/s00029-005-0013-x | mr=2215258 | year=2005 | journal=Selecta Mathematica |series=New Series | issn=1022-1824 | volume=11 | issue=3 | pages=325–347| arxiv=math/0501424 | bibcode=2005math......1424C | s2cid=10792121 }}
- {{Citation | last=Marcolli | first=Matilde | authorlink=Matilde Marcolli | title=Arithmetic noncommutative geometry | others=With a foreword by Yuri Manin | zbl=1081.58005 | series=University Lecture Series | volume=36 | location=Providence, RI | publisher=American Mathematical Society | isbn=978-0-8218-3833-4 | year=2005 }}
{{DEFAULTSORT:Bost-Connes system}}