  The Poisson geometry of a discrete string in three dimensional Euclidean
space is investigated. For this the Frenet frames are converted into a
spinorial representation, the discrete spinor Frenet equa- tion is interpreted
in terms of a transfer matrix formalism, and Poisson brackets are introduced in
terms of the spinor components. The construction is then generalised, in a
self-similar manner, into an infinite hierarchy of Poisson algebras. As an
example, the classical Virasoro (Witt) algebra that determines
reparametrisation diffeomorphism along a continuous string, is identified as a
particular sub-algebra, in the hierarchy of the discrete string Poisson
algebra.
