A model is presented for the structure and evolution of the eukaryotic and vertebrate mitochondrial genetic codes, based on the representation theory of the Lie superalgebra A(5,0) approximately sl(6/1). A key role is played by pyrimidine and purine exchange symmetries in codon quartets.
The supersymmetric model of 1] for the evolution of the genetic code is elaborated. Energy considerations in nucleic acid strand modelling, using sl(2) polarity spin and sl(2=1) family box quartet symmetry, lead for the case of codons and anticodons to assignments of codons to 64-dimensional sl(6=1) ' A(5; 0) multiplets. In a previous paper 1] we… (More)
Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map Abstract: The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a… (More)
Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding R-matrices. It is also shown that a class of generalized Heisenberg algebras including those underlying physical models such as that of Calogero-Sutherland, is… (More)
The quantum double construction of a q-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The R-matrix thus obtained is compared with the existing literature.
Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems, forming a quantum statistical model of a particle (walker) immersed in a bath of other particles (coins). Quantum walks following the so called U-and ε-quantization rules are presented. The former rule involves unitary… (More)