Spectra for infinite tensor product type actions of compact groups

Elliot C. Gootman, Aldo J. Lazar

Research output: Contribution to journalArticlepeer-review

Abstract

We present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.

Original languageEnglish
Pages (from-to)330-342
Number of pages13
JournalCanadian Journal of Mathematics
Volume48
Issue number2
DOIs
StatePublished - Apr 1996

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