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On reducibility of ultrametric almost periodic linear representations

Published online by Cambridge University Press:  18 May 2009

Bertin Diarra
Bertin Diarra
Affiliation:
Mathematiques Pures, Complexe Scientifique Des Cézeaux, 63177 Aubiere Cedex, France Fax: (33) 73.40.70.64 e-mail [email protected]
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Abstract

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Let G be a group and K be a complete ultrametric valued field. Let AP(G, K) be the algebra of the generalized almost periodic functions of G in K. We have shown in a previous paper that when AP(G, K) has an invariant mean, then any almost periodic linear representation is quasi-reducible. Here, we show that with the same hypothesis, any topologically irreducible almost periodic linear representation is finite dimensional; also, any almost periodic linear representation is the topological sum of irreducible representations. Furthermore, we obtain a Peter-Weyl theorem for the algebra AP(G, K).

We use the technical tools of Hopf algebra theory.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 83 - 98
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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