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 $G_3$, $\operatorname {RR} C^\ast (G_3))=2$.
Published
2012-03-01
How to Cite
Archbold, R. J., & Kaniuth, E. (2012). On the real rank of $C^\ast$-algebras of nilpotent locally compact groups. MATHEMATICA SCANDINAVICA, 110(1), 99-110. https://doi.org/10.7146/math.scand.a-15199
Section
Articles