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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 038, 52 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.038 (Mi sigma1575) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Quantum Statistical Mechanics of the Absolute Galois Group

Yuri I. Manina, Matilde Marcollibcd

a Max Planck Institute for Mathematics, Bonn, Germany
b University of Toronto, Toronto, Canada
c Perimeter Institute for Theoretical Physics, Waterloo, Canada
d California Institute of Technology, Pasadena, USA
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DOI: https://doi.org/10.3842/SIGMA.2020.038
Abstract: We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck–Teichmüller group, and the Drinfeld–Ihara involution.
Keywords: quantum statistical mechanics, dessins d'enfant, absolute Galois group, Drinfeld–Ihara involution, quasi-triangular quasi-Hopf algebras.
Funding agency Grant number
National Science Foundation DMS-1707882
Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN-2018-04937
RGPAS-2018-522593
The second named author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593.
Received: August 1, 2019; in final form April 15, 2020; Published online May 5, 2020
Bibliographic databases:
Document Type: Article
MSC: 11G32, 11M55, 11R32, 82B10, 82C10, 58B34
Language: English
Citation: Yuri I. Manin, Matilde Marcolli, “Quantum Statistical Mechanics of the Absolute Galois Group”, SIGMA, 16 (2020), 038, 52 pp.
Citation in format AMSBIB
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\paper Quantum Statistical Mechanics of the Absolute Galois Group
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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