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

Robert J Archbold, E. Kaniuth

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume97
Issue number1
Publication statusPublished - 2005

Keywords

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

Cite this

On the stable rank and real rank of group C*-algebras of nilpotent locally compact groups. / Archbold, Robert J; Kaniuth, E.

In: Mathematica Scandinavica, Vol. 97, No. 1, 2005, p. 89-103.

Research output: Contribution to journalArticle

@article{f23cd68c2b3940a0a55ab053f2100600,
title = "On the stable rank and real rank of group C*-algebras of nilpotent locally compact groups",
abstract = "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).",
keywords = "amenable lie-groups, star-algebras, free product, extensions, zero",
author = "Archbold, {Robert J} and E. Kaniuth",
year = "2005",
language = "English",
volume = "97",
pages = "89--103",
journal = "Mathematica Scandinavica",
issn = "0025-5521",
publisher = "Mathematica Scandinavica",
number = "1",

}

TY - JOUR

T1 - On the stable rank and real rank of group C*-algebras of nilpotent locally compact groups

AU - Archbold, Robert J

AU - Kaniuth, E.

PY - 2005

Y1 - 2005

N2 - 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).

AB - 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).

KW - amenable lie-groups

KW - star-algebras

KW - free product

KW - extensions

KW - zero

M3 - Article

VL - 97

SP - 89

EP - 103

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 1

ER -