Decomposition of (Co)isotropic Relations
Abstract
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.
Keywords
linear relation duality symplectic vector space coisotropic relationMathematics Subject Classification
Primary 18B10 Secondary 53D99Preview
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