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

• Autores: Robert J. Archbold
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 97, Nº 1, 2005, págs. 89-103
• Idioma: inglés
• DOI: 10.7146/math.scand.a-14965
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• Resumen

  • 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).