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Mathematical Notes

, Volume 82, Issue 3–4, pp 341–346 | Cite as

Nonstandard representations of locally compact groups

  • V. A. Lyubetskii
  • S. A. Pirogov
Mathematical Notes
  • 37 Downloads

Abstract

In the note, it is proved that, under natural conditions, any infinite-dimensional unitary representation T of a direct product of groups G = K × N, where K is a compact group and N is a locally compact Abelian group, is imaged by a representation of the nonstandard analog \(\tilde G\) of the group G in the group of nonstandard matrices of a fixed nonstandard size.

Key words

unitary representation nonstandard matrix imaging of groups Boolean algebra Stone space Casimir operator 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Institute for Problems of Information TransmissionRussian Academy of SciencesRussia

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