Linearizability of Poisson structures around singular symplectic leaves

Yu M. Vorobjev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The linearization problem for a Poisson structure near a singular symplectic leaf of nonzero dimension is studied. We obtain the following generalization of the Conn linearization theorem: if the transverse Lie algebra of the leaf is semisimple and compact, then the Poisson structure is linearizable, provided that certain cohomological obstructions vanish.

Original languageEnglish
Pages (from-to)780-790
Number of pages11
JournalMathematical Notes
Issue number5-6
StatePublished - Nov 2006
Externally publishedYes

Bibliographical note

Funding Information:
The author is grateful M. V. Karasev for helpful discussions during the preparation of the article. This research was supported in part by CONACYT under grant no. 43208.


  • Cohomology
  • Ehresmann connection
  • Lie-Poisson structure
  • Linearization problem
  • Poisson structure
  • Schouten bracket
  • Symplectic leaf
  • Transverse Lie algebra


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