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A constructive proof of the Peter-Weyl theorem

✍ Scribed by Thierry Coquand; Bas Spitters

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 137 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410037

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✦ Synopsis

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].

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