Locally compact abelian groups with symplectic self-duality

Details Locally compact abelian groups with symplectic self-duality Locally compact abelian groups with symplectic self-duality

2009-06-24

arxiv.org/abs/0906.4397v1

Advances in Mathematics 225 (2010) 2429-2454

Mathematics

Group Theory

23 pages

Scientific paper

10.1016/j.aim.2010.04.023

Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are found. Counterexamples are produced by studying a seemingly unrelated question about the structure of maximal isotropic subgroups of finite abelian groups with symplectic self-duality (where the original question always has an affirmative answer).

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