This article is cited in 7 papers

Deformations of vector fields and canonical coordinates on coadjoint orbits

S. P. Baranovskii, I. V. Shirokov

Irtysh Branch of Novosibirsk State Academy of Water Transport, Omsk

Abstract: We establish the concurrence of the existence of a canonical linear embedding, enabling us to pass to the Darboux coordinates on the coadjoint orbits, and the existence of a polarization of a certain linear functional. In a corollary to the main theorem we prove that every polarization is normal, which means that it satisfies the Pukansky condition.

Keywords: Lie algebra, coadjoint orbit, Lie–Poisson bracket, polarization, Pukansky condition.

UDC: 512.81+512.546.4+512.664.3

Received: 16.01.2008

 English version: Siberian Mathematical Journal, 2009, 50:4, 580–586

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