Kyoto Journal of Mathematics

Duality theorem for inductive limit groups

Nobuhiko Tatsuuma

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Abstract

In this paper, we show the so-called weak duality theorem of Tannaka type for an inductive limit–type topological group G=lim nGn in the case where each Gn is a locally compact group, and Gn is embedded into Gn+1 homeomorphically as a closed subgroup. First, we explain what a weak duality theorem of Tannaka type is and explain the difference between the case of locally compact groups and the case of nonlocally compact groups. Then we introduce the concept “separating system of unitary representations (SSUR),” which assures the existence of sufficiently many unitary representations. The present G has an SSUR. We prove that G is complete. We give semiregular representations and their extensions for G. Using them, we deduce a fundamental formula about “birepresentation” on G. Combining these results, we can prove the weak duality theorem of Tannaka type for G.

Article information

Source
Kyoto J. Math., Volume 54, Number 1 (2014), 51-73.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1394804791

Digital Object Identifier
doi:10.1215/21562261-2400274

Mathematical Reviews number (MathSciNet)
MR3178546

Zentralblatt MATH identifier
1288.22003

Subjects
Primary: 22A25: Representations of general topological groups and semigroups
Secondary: 22D35: Duality theorems

Citation

Tatsuuma, Nobuhiko. Duality theorem for inductive limit groups. Kyoto J. Math. 54 (2014), no. 1, 51--73. doi:10.1215/21562261-2400274. https://projecteuclid.org/euclid.kjm/1394804791


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References

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