On the real rank of $C^\ast$-algebras of nilpotent locally compact groups

Robert J. Archbold, Eberhard Kaniuth

Abstract


If $G$ is an almost connected, nilpotent, locally compact group then the real rank of the $C^\ast$-algebra $C^\ast (G)$ is given by $\operatorname {RR} (C^\ast (G)) = \operatorname {rank} (G/[G,G]) = \operatorname {rank} (G_0/[G_0,G_0])$, where $G_0$ is the connected component of the identity element. In particular, for the continuous Heisenberg group $G_3$, $\operatorname {RR} C^\ast (G_3))=2$.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15199

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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