In this paper, a novel discrete algebra is presented which follows by
    combining the SU(2) Lie-Poisson bracket with the discrete Frenet equation.
    Physically, the construction describes a discrete piecewise linear string in
    R3. The starting point of our derivation is the discrete Frenet frame assigned
    at each vertix of the string. Then the link vector that connect the
    neighbouring vertices assigns the SU(2) Lie-Poisson bracket. Moreover, the same
    bracket defines the transfer matrices of the discrete Frenet equation which
    relates two neighbouring frames along the string. The procedure extends in a
    self-similar manner to an infinite hierarchy of Poisson structures. As an
    example, the first descendant of the SU(2) Lie-Poisson structure is presented
    in detail. For this, the spinor representation of the discrete Frenet equation
    is employed, as it converts the brackets into a computationally more manageable
    form. The final result is a nonlinear, nontrivial and novel Poisson structure
    that engages four neighbouring vertices.

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