Groups with completely reducible regular representation

Baggett, Larry; Taylor, Keith

doi:10.1090/S0002-9939-1978-0509261-X

Groups with completely reducible regular representation
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by Larry Baggett and Keith Taylor PDF

Proc. Amer. Math. Soc. 72 (1978), 593-600 Request permission

Abstract:

Several examples are constructed of connected Lie groups with completely reducible regular representation. An example is given in each of the following classes: (i) solvable, (ii) amenable, nonsolvable, (iii) nonamenable and (iv) non-Type I. It is also shown by example that G having a completely reducible regular representation does not imply that $A(G) = {B_0}(G)$ while the reverse implication is known for separable groups (see [2] and [6]).

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Riemann-Lebesgue subsets of

and representations which vanish at infinity

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