SU(2) Lie-Poisson algebra and its descendants

@article{Dai2022SU2LA,
  title={SU(2) Lie-Poisson algebra and its descendants},
  author={Jin Dai and Theodora Ioannidou and Antti J. Niemi},
  journal={Physical Review D},
  year={2022}
}
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 R 3 . 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 is assigned the SU(2) Lie-Poisson bracket. Moreover, the same bracket defines the transfer matrices of the… 

References

SHOWING 1-5 OF 5 REFERENCES

Lectures on the geometry of Poisson manifolds

0 Introduction.- 1 The Poisson bivector and the Schouten-Nijenhuis bracket.- 1.1 The Poisson bivector.- 1.2 The Schouten-Nijenhuis bracket.- 1.3 Coordinate expressions.- 1.4 The Koszul formula and

A-Poisson structures

Let M be a paracompact differentiable manifold, A a local algebra and M^{A} a manifold of infinitely near points on M of kind A. We define the notion of A-Poisson manifold on M^{A}. We show that when

Local structure of Poisson manifolds

Varietes de Poisson et applications. Decomposition. Structures de Poisson lineaires. Approximation lineaire. Systemes hamiltoniens. Le probleme de linearisation. Groupes de fonction, realisations et

Lectures on Poisson Geometry