  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.
