Letters in Mathematical Physics

, Volume 106, Issue 12, pp 1837–1847 | Cite as

Decomposition of (Co)isotropic Relations

  • Jonathan Lorand
  • Alan WeinsteinEmail author


We identify 13 isomorphism classes of indecomposable coisotropic relations between Poisson vector spaces and show that every coisotropic relation between finite-dimensional Poisson vector spaces may be decomposed as a direct sum of multiples of these indecomposables. We also find a list of 13 invariants, each of which is the dimension of a space constructed from the relation, such that the 13-vector of multiplicities and the 13-vector of invariants are related by an invertible matrix over \({\mathbb{Z}}\). It turns out to be simpler to do the analysis above for isotropic relations between presymplectic vector spaces. The coisotropic/Poisson case then follows by a simple duality argument.


linear relation duality symplectic vector space coisotropic relation 

Mathematics Subject Classification

Primary 18B10 Secondary 53D99 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Institute of MathematicsUniversity of ZurichZurichSwitzerland

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