Groups with completely reducible regular representation-Reference-Cited by-同舟云学术

Groups with completely reducible regular representation

Published:1978 Issue:3 Volume:72 Page:593-600
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Baggett Larry,Taylor Keith

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1978-072-03/S0002-9939-1978-0509261-X/S0002-9939-1978-0509261-X.pdf

Reference9 articles.

1. A separable group having a discrete dual space is compact;Baggett, Larry;J. Functional Analysis,1972

2. A sufficient condition for the complete reducibility of the regular representation;Baggett, Larry;J. Functional Analysis,1979

3. \bysame, Riemann-Lebesgue subsets of 𝐑ⁿ and representations which vanish at infinity, J. Functional Anal. (to appear).

4. The regular representation of restricted direct product groups;Blackadar, Bruce E.;J. Functional Analysis,1977

5. L’algèbre de Fourier d’un groupe localement compact;Eymard, Pierre;Bull. Soc. Math. France,1964

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