On sufficient and necessary conditions for linearity of the transverse Poisson structure

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Cruz, I.¹ 

[1] Univ Porto, Ctr Matemat, Dept Matemat Aplicada, P-4169007 Oporto, Portugal

关键词: Poisson manifolds;    Lie algebras;   

DOI  :  10.1016/j.geomphys.2009.12.001

来源: Elsevier

【 摘 要 】

We study the possibility of bringing the transverse Poisson structure to a coadjoint orbit(on the dual of a real Lie algebra) to a normal linear form. We study the relation between two sufficient conditions for linearity of such structures (P. Molino's condition and our own). We then use these conditions to conclude that, if the isotropy subgroup of the (singular) point in question is compact, or if the isotropy subalgebra is semisimple, then there is a linear transverse Poisson structure to the corresponding coadjoint orbit. Finally, by using a natural necessary condition for linearity of such structures, we will prove that there is no polynomial transverse Poisson structure in the case of c(3)*. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free