Some remarks on self-dual locally compact Abelian groups

Corwin, Lawrence

doi:10.1090/S0002-9947-1970-0269775-4

Some remarks on self-dual locally compact Abelian groups
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Trans. Amer. Math. Soc. 148 (1970), 613-622 Request permission

Abstract:

The main results of this paper are the construction of some new self-dual locally compact Abelian groups and the proof of a structure theorem for a certain class of such groups. The construction is based on an investigation of when the extension of a compact Abelian group by its dual yields a self-dual group. It turns out that such extensions can be described algebraically ; the structure theorem follows from an analysis of the algebraic description.

References

Lorenzo Calabi, Sur les extensions des groupes topologiques, Ann. Mat. Pura Appl. (4) 32 (1951), 295–370 (French). MR 49907, DOI 10.1007/BF02417964
Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
Adam Kleppner, Multipliers on abelian groups, Math. Ann. 158 (1965), 11–34. MR 174656, DOI 10.1007/BF01370393
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
André Weil, Basic number theory, Die Grundlehren der mathematischen Wissenschaften, Band 144, Springer-Verlag New York, Inc., New York, 1967. MR 0234930
M. Rajagopalan and T. Soundararajan, Structure of self-dual torsion-free metric $\textrm {LCA}$ groups, Fund. Math. 65 (1969), 309–316. MR 247375, DOI 10.4064/fm-65-3-309-316