Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 6 January 2021 / Approved: 6 January 2021 / Online: 6 January 2021 (16:02:22 CET)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Quantum Rep. 2021, 3, 5
DOI: 10.3390/quantum3010005

Abstract

The Kummer surface was constructed in 1864. It corresponds to the desingularisation of the quotient of a 4-torus by 16 complex double points. Kummer surface is kwown 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)≅Z5⋊2O (with 2O the binary octahedral group), we now find that groups G6:=(288,69)≅Z6⋊2O and G7:=(336,118)≅Z7⋊2O 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.

Subject Areas

Kummer surface; DNA genetic code; hexamers and pentamers; informationally complete characters; finite groups; hyperelliptic curve

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