On the Lie algebra structures connected with Hamiltonian dynamical systems

• Date: 1997
• Main Authors: Smirnov, R. G., Смирнов, Р. Г.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5051
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thu...