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arXiv · 1509.04035

Decomposition of (co)isotropic relations

Jonathan Lorand·Alan Weinstein
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Abstract

We identify thirteen 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 thirteen 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.

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Jonathan Lorand, Alan Weinstein. 2015-09-14. Decomposition of (co)isotropic relations. https://doi.org/10.1007/s11005-016-0863-5

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