The regular group 𝐶*-algebra for real-rank one groups

Boyer, Robert; Martin, Robert

doi:10.1090/S0002-9939-1976-0476913-8

The regular group $C^*$-algebra for real-rank one groups
HTML articles powered by AMS MathViewer

by Robert Boyer and Robert Martin PDF

Proc. Amer. Math. Soc. 59 (1976), 371-376 Request permission

Abstract:

Let $G$ be a connected semisimple real-rank one Lie group with finite center and let $C_\rho ^{\ast }(G)$ denote the regular group ${C^{\ast }}$-algebra of $G$. In this paper a complete description of the structure of $C_\rho ^{\ast }(G)$ is obtained.

References

Claire Delaroche, Extensions des $C^*$-algèbres, Supplément au Bull. Soc. Math. France, Tome 100, Société Mathématique de France, Paris, 1972 (French). Bull. Soc. Math. France Mém., No. 29. MR 0632119
Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 0246136
Jacques Dixmier, Représentations intégrables du groupe de De Sitter, Bull. Soc. Math. France 89 (1961), 9–41. MR 140614, DOI 10.24033/bsmf.1558
A. W. Knapp, Commutativity of intertwining operators, Bull. Amer. Math. Soc. 79 (1973), 1016–1018. MR 333074, DOI 10.1090/S0002-9904-1973-13308-7
A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
Ronald L. Lipsman, Non-Abelian Fourier analysis, Bull. Sci. Math. (2) 98 (1974), no. 4, 209–233. MR 425512
Nolan R. Wallach, Cyclic vectors and irreducibility for principal series representations, Trans. Amer. Math. Soc. 158 (1971), 107–113. MR 281844, DOI 10.1090/S0002-9947-1971-0281844-2

Harmonic analysis on semisimple Lie groups