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Groups with completely reducible regular representation

1978; American Mathematical Society; Volume: 72; Issue: 3 Linguagem: Inglês

10.1090/s0002-9939-1978-0509261-x

1088-6826

Larry Baggett, Keith F. Taylor,

Advanced Algebra and Geometry

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 ) A(G) = {B_0}(G) while the reverse implication is known for separable groups (see [ 2 ] and [ 6 ]).