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Proceedings of the American Mathematical Society

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

 
 

 

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


Authors: Robert Boyer and Robert Martin
Journal: Proc. Amer. Math. Soc. 59 (1976), 371-376
MSC: Primary 22D25
DOI: https://doi.org/10.1090/S0002-9939-1976-0476913-8
MathSciNet review: 0476913
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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.


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Keywords: Semisimple Lie groups, Cartan subgroups, Weyl group, irreducible unitary representations, left regular representation, principal series, discrete series, reduced dual, hull-kernel topology, <!– MATH ${C^{\ast }}$ –> <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="${C^{\ast }}$">-algebras, restricted product
Article copyright: © Copyright 1976 American Mathematical Society