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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Groups with completely reducible regular representation


Authors: Larry Baggett and Keith Taylor
Journal: Proc. Amer. Math. Soc. 72 (1978), 593-600
MSC: Primary 22D10
DOI: https://doi.org/10.1090/S0002-9939-1978-0509261-X
MathSciNet review: 509261
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0509261-X
Article copyright: © Copyright 1978 American Mathematical Society