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Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy

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Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
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Quantum Gravity Research, Los Angeles, CA 90290, USA
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Author to whom correspondence should be addressed.
Academic Editor: Christian Corda
Quantum Rep. 2021, 3(1), 68-79; https://doi.org/10.3390/quantum3010005
Received: 6 January 2021 / Revised: 20 January 2021 / Accepted: 21 January 2021 / Published: 25 January 2021
(This article belongs to the Special Issue Groups, Geometry and Topology for Quantum Computations)
The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group G5:=(240,105)Z52O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)Z62O and G7:=(336,118)Z72O can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups G6 and G7 are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested. View Full-Text
Keywords: kummer surface; DNA genetic code; hexamers and pentamers; informationally complete characters; finite groups; hyperelliptic curve kummer surface; DNA genetic code; hexamers and pentamers; informationally complete characters; finite groups; hyperelliptic curve
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MDPI and ACS Style

Planat, M.; Chester, D.; Aschheim, R.; Amaral, M.M.; Fang, F.; Irwin, K. Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy. Quantum Rep. 2021, 3, 68-79. https://doi.org/10.3390/quantum3010005

AMA Style

Planat M, Chester D, Aschheim R, Amaral MM, Fang F, Irwin K. Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy. Quantum Reports. 2021; 3(1):68-79. https://doi.org/10.3390/quantum3010005

Chicago/Turabian Style

Planat, Michel, David Chester, Raymond Aschheim, Marcelo M. Amaral, Fang Fang, and Klee Irwin. 2021. "Finite Groups for the Kummer Surface: The Genetic Code and a Quantum Gravity Analogy" Quantum Reports 3, no. 1: 68-79. https://doi.org/10.3390/quantum3010005

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