A Novel Lie Algebra of the Genetic Code over the Galois Field of Four   DNA Bases
  By starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the principal partitions of the genetic code table were obtained as equivalent classes of quotient subspaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignment and physicochemical properties of amino acids. Moreover, a distance function defined between codons in the Lie algebra was demonstrated to have a linear behavior respect to physical variables such as the mean of amino acids energy in proteins. It was also noticed that the distance between wild type and mutant codons approach smaller values in mutational variants of four genes, i.e, human phenylalanine hydroxylase, human beta-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules in genetic code origin must be involved. 
Robersy Sanchez and Ricardo Grau