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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Group $ C\sp \ast$-algebras of real rank zero or one


Author: Eberhard Kaniuth
Journal: Proc. Amer. Math. Soc. 119 (1993), 1347-1354
MSC: Primary 46L05; Secondary 22D25
MathSciNet review: 1164146
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Abstract: Let $ G$ be a locally compact group and $ {C^{\ast}}(G)$ its group $ {C^{\ast}}$-algebra, and denote by $ \operatorname{RR} ({C^{\ast}}(G))$ the real rank of $ {C^{\ast}}(G)$. This note is a first step towards relating $ \operatorname{RR} ({C^{\ast}}(G))$ to the structure of $ G$. We identify the connected groups $ G$ with $ \operatorname{RR} ({C^{\ast}}(G)) = 0$ as precisely the compact connected ones and characterize the nilpotent groups whose $ {C^{\ast}}$-algebras have real rank zero or one.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1164146-1
PII: S 0002-9939(1993)1164146-1
Article copyright: © Copyright 1993 American Mathematical Society