Linearizability of Poisson structures around singular symplectic leaves

Yu. M. Vorob'ev<sup>ab

a</sup> Moscow State Institute of Electronics and Mathematics
^b University of Sonora

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.

UDC: 514.7

Received: 28.06.2005

DOI: 10.4213/mzm3360

 English version: Mathematical Notes, 2006, 80:6, 780–790

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