Geodesic
On reducibility of ultrametric almost periodic linear representations
Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 83-98

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Diarra, Bertin. On reducibility of ultrametric almost periodic linear representations. Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 83-98. doi: 10.1017/S0017089500030421
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