An Infinitesimal Quantum Group Underlies Classical Fluid Mechanics
Mathematical Physics
2020-10-28 v1 Soft Condensed Matter
High Energy Physics - Theory
math.MP
Abstract
Arnold showed that the Euler equations of an ideal fluid describe geodesics in the Lie algebra of incompressible vector fields. We will show that helicity induces a splitting of the Lie algebra into two isotropic subspaces, forming a Manin triple. Viewed another way, this shows that there is an infinitesimal quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.
Cite
@article{arxiv.2005.12125,
title = {An Infinitesimal Quantum Group Underlies Classical Fluid Mechanics},
author = {S. G. Rajeev},
journal= {arXiv preprint arXiv:2005.12125},
year = {2020}
}