Locally compact abelian groups with symplectic self-duality |
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Authors: | Amritanshu Prasad Ilya Shapiro |
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Affiliation: | a The Institute of Mathematical Sciences, Chennai, India b Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France c Chennai Mathematical Institute, Siruseri, India |
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Abstract: | 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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Keywords: | 22B05 |
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