矩阵遗传学，第2部分：遗传密码的简并性和具有两个准实单位的八度代数（遗传八度阴阳代数）
Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)
摘要：
分析了遗传密码的代数性质。描述了基于矩阵方法（“矩阵遗传学”）的遗传密码的研究。脊椎动物线粒体遗传密码的简并性反映在由64个三联体、20个氨基酸和终止信号组成的（8*8）-基质的黑白马赛克中。这种镶嵌遗传矩阵与特殊的8维阴阳代数及其特殊的4维情况的矩阵表示形式有关。特殊的算法，这是基于遗传分子的特征，存在的马赛克基因矩阵转换成这些代数的矩阵。用这些8维和4维代数定义了两个新的数值系统：遗传阴阳八度和遗传四度。它们与Hamilton的四元数进行了比较。讨论了新的“遗传向量计算”的要素和“遗传力学”的思想。这些代数被认为是遗传密码的模型，并作为其可能的前代码的基础。它们与阴阳二元对立有关，并为研究遗传密码的进化提供了新的机会。揭示的事实之间的关系的遗传密码和这些遗传代数讨论的想法由毕达哥拉斯：“所有的东西都是数字”。同时这些遗传代数也可以作为生物体遗传算子的代数。所描述的结果与生物信息学的代数化问题有关。他们关注这样一个问题：从代数的角度来看，生命是什么？
英文摘要：
Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20 amino acids and stop-signals. This mosaic genetic matrix is connected with the matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and of its particular 4-dimensional case. The special algorithm, which is based on features of genetic molecules, exists to transform the mosaic genomatrix into the matrices of these algebras. Two new numeric systems are defined by these 8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic tetrions. Their comparison with quaternions by Hamilton is presented. Elements of new "genovector calculation" and ideas of "genetic mechanics" are discussed. These algebras are considered as models of the genetic code and as its possible pre-code basis. They are related with binary oppositions of the Yin-Yang type and they give new opportunities to investigate evolution of the genetic code. The revealed fact of the relation between the genetic code and these genetic algebras is discussed in connection with the idea by Pythagoras: "All things are numbers". Simultaneously these genetic algebras can be utilized as the algebras of genetic operators in biological organisms. The described results are related with the problem of algebraization of bioinformatics. They take attention to the question: what is life from the viewpoint of algebra?
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