Decomposition of phase space and classification of Heisenberg groups

Details Decomposition of phase space and classification of Heisenberg groups Decomposition of phase space and classification of Heisenberg groups

2008-06-25

arxiv.org/abs/0806.4064v1

Mathematics

Group Theory

8 pages

Scientific paper

Is every locally compact abelian group which admits a Heisenberg central extension isomorphic to the product of a locally compact abelian group and its Pontryagin dual? An affirmative answer is obtained for all the commonly occurring types of abelian groups having Heisenberg central extensions, including Lie groups and certain finite Cartesian products of local fields and adeles. Furthermore, for these types of groups, it is found that the isomorphism class of the abelian group determines the Heisenberg group up to isomorphism, thereby providing a classification of such Heisenberg groups.

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