Zhukovsky-Volterra top and quantisation ideals
Abstract
In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics - the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson brackets. Using the quantisation ideal method, we have identified two distinct quantisations of the Zhukovsky-Volterra top. The first type corresponds to the universal enveloping algebras of , leading to Lie-Poisson brackets in the classical limit. The second type can be regarded as a quantisation of the four-parametric inhomogeneous quadratic Poisson pencil. We discuss the relationships between the quantisations obtained in our paper, Sklyanin's quantisation of the Euler top, and Levin-Olshanetsky-Zotov's quantisation of the Zhukovsky-Volterra top.
Cite
@article{arxiv.2405.16532,
title = {Zhukovsky-Volterra top and quantisation ideals},
author = {A. Mikhailov and T. Skrypnyk},
journal= {arXiv preprint arXiv:2405.16532},
year = {2024}
}