The group 𝐶*-algebra of the de Sitter group

Boyer, Robert; Martin, Robert

doi:10.1090/S0002-9939-1977-0473718-X

The group $C^*$-algebra of the de Sitter group
HTML articles powered by AMS MathViewer

by Robert Boyer and Robert Martin

Proc. Amer. Math. Soc. 65 (1977), 177-184

DOI: https://doi.org/10.1090/S0002-9939-1977-0473718-X

PDF | Request permission

Abstract:

Let G denote the universal-covering of the DeSitter group and ${C^\ast }(G)$ the group ${C^\ast }$-algebra of G. In this paper we use the extension theory of C. Delaroche to describe the structure of ${C^\ast }(G)$.

References

Claire Delaroche, Extensions des $C^*$-algèbres, Bull. Soc. Math. France Mém., No. 29, Société Mathématique de France, Paris, 1972 (French). Supplément au Bull. Soc. Math. France, Tome 100. 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
J. M. G. Fell, The dual spaces of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 94 (1960), 365–403. MR 146681, DOI 10.1090/S0002-9947-1960-0146681-0
J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280. MR 164248, DOI 10.1007/BF02545788
Takeshi Hirai, The characters of irreducible representations of the Lorentz group of $n$-th order, Proc. Japan Acad. 41 (1965), 526–531. MR 195989
Dragan Miličić, Topological representation of the group $C^{\ast }$-algebra of $\textrm {SL}(2,\,R)$, Glasnik Mat. Ser. III 6(26) (1971), 231–246 (English, with Serbo-Croatian summary). MR 308795
Kiyosato Okamoto, On the Plancherel formulas for some types of simple Lie groups, Osaka Math. J. 2 (1965), 247–282. MR 219668
Reiji Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France 91 (1963), 289–433 (French). MR 179296, DOI 10.24033/bsmf.1598
Ernest A. Thieleker, The unitary representations of the generalized Lorentz groups, Trans. Amer. Math. Soc. 199 (1974), 327–367. MR 379754, DOI 10.1090/S0002-9947-1974-0379754-8

Harmonic analysis on semisimple Lie groups