Groups with completely reducible regular representation
HTML articles powered by AMS MathViewer
- 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]).References
- Larry Baggett, A separable group having a discrete dual space is compact, J. Functional Analysis 10 (1972), 131–148. MR 0346090, DOI 10.1016/0022-1236(72)90045-6
- Larry Baggett and Keith Taylor, A sufficient condition for the complete reducibility of the regular representation, J. Functional Analysis 34 (1979), no. 2, 250–265. MR 552704, DOI 10.1016/0022-1236(79)90033-8 —, Riemann-Lebesgue subsets of ${{\mathbf {R}}^n}$ and representations which vanish at infinity, J. Functional Anal. (to appear).
- Bruce E. Blackadar, The regular representation of restricted direct product groups, J. Functional Analysis 25 (1977), no. 3, 267–274. MR 0439979, DOI 10.1016/0022-1236(77)90073-8
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
- Alessandro Figà-Talamanca, Positive definite functions which vanish at infinity, Pacific J. Math. 69 (1977), no. 2, 355–363. MR 493175
- Idriss Khalil, Sur l’analyse harmonique du groupe affine de la droite, Studia Math. 51 (1974), 139–167 (French). MR 350330, DOI 10.4064/sm-51-2-139-167
- George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423
- Giancarlo Mauceri and Massimo A. Picardello, Noncompact unimodular groups with purely atomic Plancherel measures, Proc. Amer. Math. Soc. 78 (1980), no. 1, 77–84. MR 548088, DOI 10.1090/S0002-9939-1980-0548088-9
Additional Information
- © Copyright 1978 American Mathematical Society
- 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