A constructive proof of the Peter-Weyl theorem

T. Coquand, B.A.W. Spitters

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)

    Abstract

    We present a new and constructive proof of the Peter-Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*-algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2].
    Original languageEnglish
    Pages (from-to)351-359
    JournalMathematical Logic Quarterly
    Volume51
    Issue number4
    DOIs
    Publication statusPublished - 2005

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