Matrix genetics, part 3: the evolution of the genetic code from the   viewpoint of the genetic octave Yin-Yang-algebra
  The set of known dialects of the genetic code (GC) is analyzed from the viewpoint of the genetic octave Yin-Yang-algebra. This algebra was described in the previous author's publications. The algebra was discovered on the basis of structural features of the GC in the matrix form of its presentation ("matrix genetics"). The octave Yin-Yang-algebra is considered as the pre-code or as the model of the GC. From the viewpoint of this algebraic model, for example, the sets of 20 amino acids and of 64 triplets consist of sub-sets of "male", "female" and "androgynous" molecules, etc. This algebra permits to reveal hidden peculiarities of the structure and evolution of the GC and to propose the conception of "sexual" relationships among genetic molecules. The first results of the analysis of the GC systems from such algebraic viewpoint say about the close connection between evolution of the GC and this algebra. They include 8 evolutionary rules of the dialects of the GC. The evolution of the GC is appeared as the struggle between male and female beginnings. The hypothesis about new biophysical factor of "sexual" interactions among genetic molecules is put forward. The matrix forms of presentation of elements of the genetic octave Yin-Yang-algebra are connected with Hadamard matrices by means of the simple U-algorithm. Hadamard matrices play a significant role in the theory of quantum computers, in particular. It gives new opportunities for possible understanding the GC systems as quantum computer systems. Revealed algebraic properties of the GC permit to put forward the problem of algebraization of bioinformatics on the basis of the algebras of the GC. Our investigation is connected with the question: what is life from the viewpoint of algebra? The algebraic version of the origin of the GC is discussed. 
Sergey V. Petoukhov