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.

中文翻译：

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流体力学中螺旋性的无穷小量子群

阿诺德表明，理想流体的欧拉方程描述了不可压缩矢量场李代数中的测地线。我们将证明螺旋性导致李代数分裂成两个各向同性的子空间，形成一个马宁三元组。从另一个角度来看，这表明在经典流体力学的基础上存在一个无穷小的量子群（又名李双代数）。