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46 papers · 1 filter
Manifolds of vortex loops as coadjoint orbits
Ioana Ciuclea, Cornelia Vizman
We study a class of coadjoint orbits of the area preserving diffeomorphism group of the plane consisting of vortex loops, namely closed curves in the plane decorated with one-forms…
Nonlinear Grassmannians: plain, decorated, augmented
Stefan Haller, Cornelia Vizman
Decorated and augmented nonlinear Grassmannians can be used to parametrize coadjoint orbits of classical diffeomorphism groups. We provide a general framework for decoration and au…
Constructing Ricci vector fields on with a diagonal metric
Adara M. Blaga
We put into light Ricci vector fields on endowed with a diagonal metric.
Certain symmetries of with diagonal metrics
Adara M. Blaga
We put into light the Killing vector fields on endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lamé coefficients, we co…
Universal central extension of the Lie algebra of exact divergence-free vector fields
Bas Janssens, Leonid Ryvkin, Cornelia Vizman
We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the anal…
NL bialgebras
Zohreh Ravanpak
In this paper, we introduce the concept of (weak) NL bialgebras. These structures consist of a Lie bialgebra $(\g,[\cdot,\cdot],δ)$ equipped with a Nijenhuis structure on the Lie a…