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Continuity conditions for finite-dimensional representations of some locally bounded groups. (English) Zbl 1117.22003

The author proves necessary and sufficient conditions for the continuity of finite-dimensional representations of some topological groups. The conditions are formulated in terms of the variation of the representation at the identity of the group. The conditions are found for the following groups:
– locally oddly divisible groups;
– topological groups in which the open normal subgroups form a neighborhood base of the identity;
– almost divisible, non-discrete, locally pseudo-compact groups;
– (almost) connected locally compact groups.
An application of the above result to the approximation of continuous quasirepresentations of almost connected locally compact groups is given.

MSC:

22D12 Other representations of locally compact groups
22D05 General properties and structure of locally compact groups
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