Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 072, 10 pages      arXiv:1503.00169      https://doi.org/10.3842/SIGMA.2015.072
Contribution to the Special Issue on Poisson Geometry in Mathematics and Physics

(Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces

Jonathan Lorand a and Alan Weinstein b
a) Department of Mathematics, ETH Zurich, Zurich, Switzerland
b) Department of Mathematics, University of California, Berkeley, CA 94720 USA

Received March 01, 2015, in final form September 03, 2015; Published online September 10, 2015

Abstract
We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector spaces. We identify ten elementary types which are the building blocks of such pairs, and we write down a matrix, invertible over $\mathbb{Z}$, which takes one 10-tuple of invariants to the other.

Key words: coisotropic subspace; direct sum decomposition; Poisson vector space; presymplectic vector space.

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