On the stable rank and real rank of group C*-algebras of nilpotent locally compact groups

Robert J Archbold, E. Kaniuth

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It is shown that if G is an almost connected nilpotent group then the stable rank of C* (G) is equal to the rank of the abelian group G/[ G, G]. For a general nilpotent locally compact group G, it is shown that finiteness of the rank of G/[G, G] is necessary and sufficient for the finiteness of the stable rank of C*(G) and also for the finiteness of the real rank of C*(G).

Original languageEnglish
Pages (from-to)89-103
Number of pages14
JournalMathematica Scandinavica
Issue number1
Publication statusPublished - 2005


  • amenable lie-groups
  • star-algebras
  • free product
  • extensions
  • zero

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