Group $C^ \ast$-algebras of real rank zero or one
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- by Eberhard Kaniuth PDF
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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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1347-1354
- MSC: Primary 46L05; Secondary 22D25
- DOI: https://doi.org/10.1090/S0002-9939-1993-1164146-1
- MathSciNet review: 1164146