Poisson hierarchy of discrete strings

•Witt (classical Virasoro) algebra is derived in the case of discrete string.•Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings.•Spinor representation of discrete Frenet equations is developed.

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 equation 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.