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

• Type: Article in International Scientific Journal
• Date: 2010

Authors

Cruz, I (Author) FCUP; Fardilha, T (Author) Other

Journal

Title: Journal of Geometry and Physics

Vol. 60

Pages: 543-551

ISSN: 0393-0440

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-8RN

DOI: 10.1016/j.geomphys.2009.12.001

Abstract (EN): 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)*.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9