Linearizability of Poisson structures around singular symplectic leaves

Yu M. Vorobjev

doi:10.1007/s11006-006-0201-9

Linearizability of Poisson structures around singular symplectic leaves

Yu M. Vorobjev^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	780-790
Number of pages	11
Journal	Mathematical Notes
Volume	80
Issue number	5-6
DOIs	https://doi.org/10.1007/s11006-006-0201-9
State	Published - Nov 2006
Externally published	Yes

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.

Keywords

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

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10.1007/s11006-006-0201-9

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title = "Linearizability of Poisson structures around singular symplectic leaves",

abstract = "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.",

keywords = "Cohomology, Ehresmann connection, Lie-Poisson structure, Linearization problem, Poisson structure, Schouten bracket, Symplectic leaf, Transverse Lie algebra",

author = "Vorobjev, {Yu M.}",

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.",

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AU - Vorobjev, Yu M.

N1 - 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.

PY - 2006/11

Y1 - 2006/11

N2 - 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.

AB - 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.

KW - Cohomology

KW - Ehresmann connection

KW - Lie-Poisson structure

KW - Linearization problem

KW - Poisson structure

KW - Schouten bracket

KW - Symplectic leaf

KW - Transverse Lie algebra

UR - http://www.scopus.com/inward/record.url?scp=33845608161&partnerID=8YFLogxK

U2 - 10.1007/s11006-006-0201-9

DO - 10.1007/s11006-006-0201-9

M3 - Artículo

SN - 0001-4346

VL - 80

SP - 780

EP - 790

JO - Mathematical Notes

JF - Mathematical Notes

IS - 5-6

ER -

Linearizability of Poisson structures around singular symplectic leaves

Abstract

Bibliographical note

Keywords

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