Galois groups and genetic code

Abstract

This article was inspired by the inverse problem of Galois theory. Galois groups are realized
as number theoretic symmetry groups realized physically in TGD a symmetries of space-time
surfaces. Galois confinement as an analog of color confinement is proposed in TGD inspired
quantum biology .
Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view
of cognition. The TGD based model of the genetic code involves in an essential manner the
groups A5 (icosahedron), which is the smallest non-abelian simple group, and A4 (tetrahedron).
The identification of these groups as Galois groups leads to a more precise view about genetic
code. The question why the genetic code is a fusion of 3 icosahedral codes and of only a
single tetrahedral code remained however poorly understood.
The identification of the symmetry groups of the I, O, and T as Galois groups makes
it possible to answer this question. Icosa-tetrahedral tesselation of 3-D hyperbolic space
H3
, playing central role in TGD, can be replaced with its 3-fold covering replacing I/O/T
with the corresponding symmetry group acting as a Galois group. T has only a single
Hamiltonian cycle and its 3-fold covering behaves effectively as a single cycle. Octahedral
codons can be regarded as icosahedral and tetrahedral codons so they do not contribute to
the code.