Galois groups and genetic code

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 centrl 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  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.

See the article Galois groups and genetic code.

For a summary of earlier postings see Latest progress in TGD.

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