Dublin Institute for Advanced Studies 00353 (0) 16140100

S. G. Rajeev (University of Rochester)

Title: Helicity leads to a Quantum Group in Classical Hydrodynamics

Abstract: Helicity is the integral of the dot product of velocity and vorticity. It is famous as a conserved quantity of three dimensional hydrodynamics, shown by Moffat to be the average linking number of fluid paths. It is also an invariant inner product (not positive) in  the Lie algebra of incompressible vector fields. I will show that there are two sub-Lie-algebras dual to each other under this inner product, which form  a Manin triple. This shows that the the set of incompressible vector fields is a Lie bi-algebra or infinitesimal quantum group in the language of Drinfeld. When the fluid satisfies periodic boundary conditions, this Lie algebra also admits a central extension, making it an appealing generalization of the Virasoro algebra to three dimensions. http://arxiv.org/abs/2005.12125v1

Talk – Video

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