Hamiltonian Systems on Quantum Spaces

Abstract

In this paper we consider Hamiltonian systems on the quantum plane and we show that the set of Q-meromorphic Hamiltonians is a Virasoro algebra with central charge zero and the set of Hamiltonian derivations of the algebra of $Q$-analytic functions ${\mathcal{A}}_q$ with values in the algebra of $Q$-meromorphic functions ${\mathcal{M}}_q$ is the Lie algebra $sl(2,A_1(q)).$ Moreover we will show that any motion on a quantum space is associated with a quadratic Hamiltonian.

18 pages, LaTeX, no figures

References in corpus (2)

• Lagrangian formulation of some q-deformed systems
• Lagrangian and Hamiltonian Formalism on a Quantum Plane