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Communications in Mathematical Physics

, Volume 283, Issue 3, pp 729–748 | Cite as

Group Orbits and Regular Partitions of Poisson Manifolds

  • Jiang-Hua Lu
  • Milen YakimovEmail author
Article

Abstract

We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties \({\mathcal {L}}\) of Lagrangian subalgebras of reductive quadratic Lie algebras \({\mathfrak {d}}\) with Poisson structures defined by Lagrangian splittings of \({\mathfrak {d}}\) . In the special case of \({\mathfrak {g} \oplus \mathfrak {g}}\) , where \({\mathfrak {g}}\) is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on \({\mathcal {L}}\) defined by arbitrary Lagrangian splittings of \({\mathfrak {g} \oplus \mathfrak {g}}\) . Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin–Drinfeld splittings as special cases.

Keywords

Poisson Structure Closed Subgroup Poisson Manifold Symplectic Leave Regular Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Hong KongPokfulamHong Kong
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

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