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Journal Article

Linear phase space deformations with angular momentum symmetry

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Meneses,  Claudio
Max Planck Institute for Mathematics, Max Planck Society;

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1803.08895.pdf
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Meneses, C. (2019). Linear phase space deformations with angular momentum symmetry. Journal of Geometric Mechanics, 11(1), 45-58. doi:10.3934/jgm.2019003.


Cite as: https://hdl.handle.net/21.11116/0000-0005-0DD8-A
Abstract
Motivated by the work of Leznov-Mostovoy, we classify the linear deformations of standard $2n$-dimensional phase space that preserve the obvious symplectic $\mathfrak{o}(n)$-symmetry. As a consequence, we describe standard phase space, as well as $T^{*}S^{n}$ and $T^{*}\mathbb{H}^{n}$ with their standard symplectic forms, as degenerations of a 3-dimensional family of coadjoint orbits, which in a generic regime are identified with the Grassmannian of oriented 2-planes in $\mathbb{R}^{n+2}$.